Probability Concepts folder
₃P₂🔸
3
₆C₄
15
Evaluate ₁₄C₅.🔸
2,002
There are 4 choices for skis, 2 choices for bindings, and 5 choices for boots. How many ways can skis, bindings, and boots be chosen?
40
What is ₁₂C₅?
495
₁₂C₈
495
5! x 0!/(4 - 1)!
5
At a deli, you have a choice of turkey, roast beef, or ham on your sandwich and a choice of potato chips or corn chips on the side. How many different ways can you order a sandwich and chips?🔹
6
Evaluate: ₈C₄
70
spinning a 7 on a spinner three times in a row
Independent
Which of the following is an outcome for flipping a coin and then rolling a 6-sided number cube?
T, 2
What is the relationship between ₁₀C₇ and ₁₀C₃?
They are equal.
choosing the winner and runner-up at a dog show
dependent
both red
⁹/₁₀₀
If a person draws 2 cards at random from a standard deck of 52 cards, what is the probability that they get 2 aces?
🚫1/1,326
Which of the following best describes: P(exactly one is a 30)
1/780
tossing a coin and rolling a number cube
12
₈C₈
1
What is the probability of rolling a 3 or an even number when a standard six-sided number cube is tossed? [______]
-2/3
8 people from a group of 12 [___________]
-495
events for which the outcome of one event does not affect the probability of the other [__________________________]
-independent events
The graph shows the dogs bathed at a dog-grooming business one day. What is the probability that the first two dogs bathed were large dogs?
12/145
Find: 5P4
120
A student is chosen at random from a class of 10 boys and 20 girls. What are the odds that a boy is chosen?
1:2
From a group of 10 people, 5 are selected at random to participate in a game show. In how many ways can the 5 people be selected?🔸
252
₃₂₅C₁
325
₅P₂
60
The students in gym class each pick lockers for their own use. Juanita picks her locker, and then Serina chooses a locker.
Dependent
A coin is tossed. P(head or tail)
Mutually exclusive; 1/2
Odds can be written as a fraction, percent, or decimal.
T
Odds compare two quantities.
T
a! + b! = b! + a!
T
Which situation will have the greatest number of possible outcomes?
The number of 5-digit zip codes, where the digits can be repeated.
Which situation gives you the most possible outcomes?
You choose 3 people out of 10 people.
Odds can
be greater than one
P(a red card or a queen)
inclusive, 15/26
P(a 7 or a heart)
inclusive, 4/13
Pulling a sock from a drawer, replacing the sock, and pulling another sock from a drawer at random is an example of __________.
independent events
Identify the expression below that represents mPn.
m!/(m - n)!
P(ace or club)
mutually exclusive, 17/52
Two events are independent when the following is true:
the outcome of one event does NOT determine the outcome of the other event
What is the probability that the first spinner will land on B, the second spinner will land on 3, and the third spinner will land on Green?
¹/₂₄
P(4, then 4)
¹/₂₅
9!/7!•2!
36
Evaluate: 4!/3!1! x 9!/5!4!
504
Seven cards are drawn in succession and without replacement from a standard deck of 52 cards. How many sets of seven cards are possible?
133,784,560
Each of the numbers from 1 to 50 is written on a tile and the tiles are placed upside down on the top of a table. If a tile is picked up at random, what is the probability that the number on the tile is a multiple of 7 or a multiple of 8?
13/50
choosing a letter from the word SPACE and choosing a consonant from the word MATH🔹
15
How many different arrangements can be made using all of the letters in the word IOWA?
24
Hunter is a big fan of the Houston Astros baseball team and wears a different jersey and cap every time he goes to a game. The table shows the number of jerseys and caps that Hunter owns. How many jersey/cap combinations can Hunter wear?
24
In how many ways can 5 toy animals be arranged in a line on a shelf if one of the toys is a tortoise and it must be at the end of the line?
24
You roll a number cube twice.🔹
36 outcomes
Find: 6P4
360
The weatherman says there is a 30% chance of rain tomorrow. Find the odds that it will rain tomorrow.
3:7
a dime and a quarter are tossed
4
There are 9 children playing in a playground. In a game, they all have to stand in a line such that the youngest child is at the beginning of the line. How many ways can the children be arranged in the line?
40,320
A shirt company has 3 designs each of which can be made with short or long sleeves. There are 7 color patterns available. How many
42
Evaluate: ₁₀C₂
45
A jar contains 3 chocolate cookies, 5 peanut butter cookies, and 6 coconut cookies. If 3 cookies are selected in succession, what is the probability of selecting chocolate, then peanut butter, and then coconut cookies, if replacement occurs each time?🔹
45/1372
A sandwich shop has 8 meats and 6 kinds of bread. How many different sandwiches can be made using one type of meat and one type of bread?
48
If a 6-sided number cube is also rolled, how many outcomes are possible?
48
In a refrigerator, there are 6 bottles of soft drinks (each a different brand) and 8 cans of juice (each a different type). How many combinations can be made with one soft drink and one fruit drink?
48
The letters in Montgomery, Alabama are written on slips of paper, one letter per slip. What are the odds of drawing an A?
4:13
Each card in a set of 7 cards has one letter from the word Florida. What are the odds of choosing a card that does not have a vowel?
4:3
A bag contains five green marbles and four red marbles. The marbles are randomly selected one at a time. What are the odds in favor of picking the green marble on the first selection?🔹
5 to 4
Which events are mutually exclusive?
choosing a jack and a numbered card (2 through 10) from a standard deck of cards
You roll a die and toss a penny.
(1, H), (2, H), (3, H), (4, H), (5, H), (6, H), (1, T), (2, T), (3, T), (4, T), (5, T), (6, T)
Ashley takes her 3-year-old brother Alex into an antique shop. There are 5 statues, 4 picture frames, and 3 vases on a shelf. Alex accidentally knocks 2 items off the shelf and breaks them. Choose the probability best described by: 1/22 [__________________________________________________]
-P(breaking 2 picture frames)
events for which the outcome of the first event affects the probability of the second event [_________________________]
-dependent events
Alan's online test has 10 true-false questions and 5 multiple-choice questions. Each multiple-choice question has 4 different answer choices. How many different choices for answering the 15 questions are possible?
1,048,576
Three computers are randomly selected and tested. What is the probability that all three are defective if the first and second ones are not replaced after being tested?
1/1140
What is the probability of getting a 6 each time if a die is rolled 4 times?
1/1296
What is the probability of getting tails each time if a coin is tossed 4 times?
1/16
8 men and 6 women arrive separately in a random fashion to a meeting. What is the probability that the first 4 people to show up are men?
1/2
Evaluate: ₆C₃
20
Suppose you choose a letter at random from the word Indiana. What are the odds that the letter you choose will be an a?
2:5
How many different ways can 4 people be seated around a circular table?
6
P(number greater than 5 and heads) ▢ P(prime number and tails)
<
P(3 and tails) ▢ P(5 and heads)
=
When two dice are rolled, 36 equally likely outcomes are possible as shown below. (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6) (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6) (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6) (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6) (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) Let x be the product of the numbers. Let P be the probability of the desired outcome. Compare the following charts and determine which chart shows the probability distribution for the product of the two numbers.
Chart A x_|2_|3__|4_|5 _|6_|7_|8_|9_|10_|11_|12_| Px|¹/₆|¹/₁₈|¹/₁₂|¹/₉|⁵/₃₆|¹/₆|⁵/₃₆|¹/₉|¹/₁₂| ¹/₁₈ | ¹/₃₆ |
(a!)^b = a ^b!🔸
F
Odds and probability are the same thing.
F
Probability is just another word for "odds".
F
A card is drawn from a standard deck of cards. P(6 or ace)
Mutually exclusive; 2/13
A card is drawn from a standard deck of cards. P(queen or jack)
Mutually exclusive; 2/13✔️
Does this table represent a probability distribution? Explain your answer.
No, because the sum of the probabilities is more than one.
Which of the following formulas applies to independent events?
P(A ∩ B) = P(A) • P(B)
What does the notation ₇C₃ represent?
The number of ways to choose 3 items out of 7, where order doesn't matter.
Which of the following statements is true for permutations?
The order of objects counted in a permutation always matters.
In a single experiment, a die is tossed and a spinner with the letters A, B, and C is spun. Each letter is equally likely. Find the sample space and then find the probability of getting a B.
The sample space is 18. The probability of getting a B is 1/3.
To find the probability of something happening or not happening you must know
all of the above
There is only one copy of each of the 25 magazines in the school library. Peter and Tanya go to the library and each choose one magazine. Peter gets to the library first and chooses Newsweek. When Tanya arrives, she chooses Time.
dependent events
There are 3 literature books, 4 geography books, and 3 science books on a shelf. If 3 books are chosen at random one after the other, what is the probability that a literature book, a geography book, and a science book are selected if replacement does not take place?
dependent; 1/20
A bag contains 4 black, 5 red, and 6 pink balls. If 3 balls are selected one after the other without replacement, what is the probability that 3 red balls are chosen?
dependent; 2/91
P(a 4 or a club)
inclusive, 4/13✔️
choosing the color and size of a pair of shoes
independent
a multiple of 3 or a multiple of 4
²/₃ *¹/₂
At a party, there are 2 six-packs of regular cola, 1 six-pack of diet cola, 1 six-pack of cherry cola, and 1 six-pack of vanilla cola. If a can of cola is chosen at random, what is the probability it will be a cherry cola or a vanilla cola?
²/₅
What is the probability of the coin landing tails up both times?
¹/₄
You spin a spinner with four equal sections labeled 1, 2, 3, and 4 and toss a dime.
(1, H), (2, H), (3, H), (4, H), (1, T), (2, T), (3, T), (4, T)
In how many ways can the letters M, N, O, P, and Q be ordered?
120
According to the 2000 U.S. Census Bureau, 49.65% of Texas residents were male. If one Texan was selected at random in 2000, what is the probability he was male?
0.4965
As part of Ella's birthday present, her mother tells her she can choose two days, Monday through Friday, that she doesn't have to do her chores. How many combinations of days can she choose?
10
Determine the number of ways to choose a set of 9 pencils from a selection of 10.
10
A personal identification code consists of five digits (0 through 9). How many codes are possible?
100,000
A movie rental store has a movie selection that consists of 4 action movies, 3 horror movies, 2 drama movies, and 3 comdies. If you select two movies at random, what is the probability that you select 2 action movies?
11
How many combinations of two books can be chosen from a group of four on a shelf?
12
How many outcomes are possible? (coin, tile)
12
picking a number from 1 to 4 and choosing the color red, green, or yellow
12
rolling a number cube and choosing one of two cards marked X and Y
12
small, medium, large, and extra large in blue, red, or green
12
How many different arrangements can be made using all of the letters in the word TOPIC?
120
In how many ways can 6 members of a dance group in different color costumes be made to stand in a line if the first person is in a yellow costume?
120
Tom goes to a stationery shop to purchase a set of watercolors and a paintbrush. There are 3 different brands of watercolors each available in 2 different size packs. There are 2 brands of paintbrushes each available in 8 different sizes. How many ways Tom can choose a pack of watercolors and a paintbrush?
16
choosing a purple, green, black or silver mountain bike having 10, 18, 21 or 24 speeds
16
You toss a coin four times.
16 outcomes
What is the probability that Holly will not be chosen?
167/170
What are the odd's against Holly being chosen?
170/3
What is the probability that Oscar will not win?
174/175
What are the odds against Oscar winning?
175/1
A student is chosen at random from a class of 10 boys and 20 girls. What are the odds that a girl is not chosen?
1:2
Find the odds of a coin landing heads up when you toss a coin?
1:2
You buy a raffle ticket to win a computer. One of 200 tickets will be drawn from a box to determine the winner. What are the odds that you win?
1:200
8 people meet, and each person shakes every other person's hand once. How many handshakes occurred?
28
The probability of choosing a red marble from a bag of marbles is 2/5. What are the odds of choosing a red marble from the bag?
2:3
Suppose you roll a standard number cube. What are the odds that the number is a multiple of 3?
2:4
If you flip a coin ten times, how many different sequences of heads and tails are possible?
2¹⁰ = 1024
John, Keri, and Carlos are working on a project for school. How many ways can they decide which two of them will give the oral report to the class?
3
Suppose you have more than one kind of shirt and more than one pair of jeans. Which of the following could NOT be the total number of outfits you can make?
3
A bag contains 30 red tiles, 15 green tiles, and 5 yellow tiles. One tile is drawn and then replaced. Then a second tile is drawn. What is the probability that the first tile is yellow and the second tile is green?
3%
From a group of 5 freshmen, 3 sophomores, 4 juniors, and 3 seniors, how many 5-person committees are possible?
3,003
John is getting his ATM card activated. He must select a password containing 4 nonzero digits to be able to use the card. How many passwords are allowed if no digit may be used more than once?🔹
3,024
What are the odds in favor of James being chosen?
5/15
What is the probability of drawing a p or a vowel in the word palindrome? Hint: Determine if events happen at the same time.
5/26
A store has 11 kinds of bagels and 5 kinds of spreads. How many different combinations of a bagel and 1 spread can be made?
55
Victor and Akira are part of a group going to a wrestling match. The group has 3 ringside seats, 3 bleacher seats, and 4 seats in the mezzanine. If the group randomly chooses their seats, what is the probability that both Victor and Akira will sit ringside at the wrestling match?
6.7%
An investor would like to invest $60,000 in 2 stocks from a list of 6 suggested by a broker. How many investments of $30,000 each are possible?
64
If 6 newborn babies are randomly selected, how many different gender sequences are possible?
64
In a high school, a student has an option of 3 foreign languages, training for 4 different musical instruments, and 6 types of outdoor activities. How many ways can a student select a foreign language, an instrumental training, and an outdoor activity?
72
A die is rolled 30 times. What is the probability of getting x even numbers?
Binomial probability; n = 30, p = 0.5, q = 0.5
What does the symbol for factorial function (n!) mean?
It means to multiply a series of descending natural numbers.
Please select the best answer from the choices provided
🚫¹/₁₅🚫²/₁₅
Given ₄C₂, I first apply the formula for combinations, which gives ₄C₂ = 4!/2! (4 - 2)!. This expression simplifies to ₄C₂ = 4!/(2 • 4 - 2 • 2)! = 4!/(8 - 4)! = 4!/4!. Evaluating this, I get a final answer of 1.
The simplification step is incorrect.
Decide if the following problem is an example of a permutation or a combination. State your rationale. For a study, 4 people are chosen at random from a group of 10 people. How many ways can this be done?
combination - an unordered arrangement of objects
A bag contains 4 marbles. You draw a red marble, put it back in the bag, and then draw a blue marble.
independent events
Find P(tails, vowel).
¹/₄, 0.25, 25%
P(even number, red)
¹/₅
In a certain game, a player throws a standard 6-sided number cube twice per turn. What is the probability that the result of the first throw will be a 5 or a 6, and the result of the second throw will be an even number?
¹/₆
What is the probability that the first spinner will land on an odd number and the second spinner will land on a vowel?🔹
¹/₆
(7 - 5)!
2
A factory manufactures plastic bottles of 4 different sizes, 3 different colors, and 2 different shapes. How many different combinations are possible?
24
A garment company has been contracted to make uniforms for players of a football tournament. There are 12 different colors and 12 designs selected for the uniforms. How many combinations of colors and designs can be made for the uniforms of different teams?
24
choosing black, blue or brown socks with boots, gym shoes or dress shoes
9
Which of the following is not a binomial experiment?
Asking 100 people what their favorite color is.
Probability can🔹
not be greater than one
When dealing with the occurrence of more than one event, what is one way to determine all possible combinations?
sample space
How many distinct committees of 13 people can be formed if the people are drawn from a pool of 20 people? Use factorials to express the answer.
₂₀C₁₃ = 20!/7!13!
Joe wants to buy a pair of shoes. His shoe size is available in 4 designs and 5 colors in a particular shop. From how many combinations of designs and colors can he choose?
20
There are 10 yogurt flavors, 4 syrups, and 5 toppings. How many ways can one flavor, one syrup, and one topping be chosen?
200
What is the value of ₇C₅? [____]
21
How many different groups of 3 movies can a person rent if there are 12 movies to choose from?
220
A circular, rotating serving tray has 5 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the tray?🔸
24
Each spinner is spun once. Find the probability of spinning blue both times.
24
6!•8!/7!•4!
240
Find: 7P5
2520
A card is picked at random from a standard deck of 52 cards. What is the probability of picking a face card (King, Queen, or Jack)?
3/13
What is the probability that Holly will be chosen?
3/170
Three computers are randomly selected and tested. What is the probability that none are defective if the first and second ones are not replaced after being tested?
34/57
A circular, rotating serving tray has 8 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the tray?
5040
A yogurt shop offers 6 different flavors of frozen yogurt and 9 different toppings. How many choices are possible for a single serving of frozen yogurt with one topping?
54 choices
Craig stops at a gas station to fill his tank. He must choose between full-service and self-service and between regular, midgrade and premium gasoline. How many possible combinations are there?
6
What is the sample space of the experiment? What is the probability of getting a 1 or a 2?
6 possible outcomes; P(1 or 2) = 1/3
₉P₆🔸
60480
How many different license plates are possible if a license plate consists of 2 capital letters followed by 5 digits?
67,600,000
How many outcomes are possible? (coin, spinner)
8
tossing a quarter, a nickel and a dime
8
Which calculation would you use to find ₈P₅?
8 x 7 x 6 x 5 x 4
Phone numbers consist of a three-digit area code followed by seven digits. If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, how many different phone numbers are possible? How did you come up with your answer?🔹
8 • 2 • 10 • 8 • 10 • 10 • 10 • 10 • 10 • 10 = 1,280,000,000
A box contains 6 nuts, 8 bolts, and 4 screws. If 3 objects are selected in succession randomly, what is the probability of selecting a nut, then a bolt, then a screw, if replacement occurs each time?
8/243
a multiple of 2 or a multiple of 5🔹
²/₃✔️
P(odd, then odd)
⁹/₂₅
At a soccer game, a coin is tossed that comes up heads. At the next game, the same coin is tossed and it comes up heads again.🔹 [_____________________]
-independent
You get three 4's on three rolls of a number cube. [_____________________]
-independent
The names of all the people at a party one night are put into a hat for a raffle. The first name picked wins the grand prize and is not eligible for any other prizes. The second name picked wins the runner-up prize. [_____________________]
-not independent
Suppose that the probability a seed will germinate is 85%. What is the probability that 7 of these seeds will germinate when 10 are planted?
0.1298
In a randomly generated sequence of 24 binary digits (0s and 1s), what is the probability that exactly half of the digits are 0?
0.1612
Suppose that the probability a seed will germinate is 80%. What is the probability that 7 of these seeds will germinate when 10 are planted?
0.201
According to the 2000 U.S. Census Bureau, 49.65% of Texas residents were male. If one Texan was selected at random in 2000, what is the probability she was female?🔸
0.5035
What is the theoretical probability of the event that a family with two children has one boy and one girl? Make a tree diagram to help solve the problem.
1/2
What is the probability of getting a 4 each time if a die is rolled 3 times?
1/216
A game is played where 26 tiles are in a bag. Each tile has a different letter of the alphabet on it. If you draw 5 letters, what is the probability of the letters being M-U-S-I-C in order, if there is no replacement?
1/7,893,600
At Healthy Option Family Restaurant, kids can get a number of kiddy meal choices. Refer to the tree diagram. How many different kinds of kiddy meals are there?
12
How many possible outcomes are there for each toss?
2
A student ID number is a letter of the alphabet followed by 2 digits. How many different IDs are possible if the digits can be repeated?
2,600
A toy factory makes a red toy, a green toy, and a blue toy. In a lot of 2,500 toys, 500 were red, 1,500 were green, and 500 were blue. The toy factory has a defect rate of 4%, regardless of the color. If a toy is chosen at random, what is the probability it is blue or red, and defective?
2/125
Javier's movie collection consists of 3 action movies, 5 comedies, and 9 dramas. In a rush, he randomly grabs 3 movies to bring on a plane flight. What is the probability that he chose 2 action movies and 1 comedy?
3/136
For a college debate competition, Daniel must select one topic of six topics to speak at the first level. He must also select a different topic from the same list to speak at the second level of the competition. How many ways can he choose the topics for the two levels?
30
A ZIP code contains 5 digits. How many different ZIP codes can be made with the digits 0 through 9 if no digit is used more than once?
30,240
You win a prize at a carnival. You can pick 5 prizes off the first shelf, 3 prizes off the second shelf, or 1 prize off the third shelf. You decide to take the first shelf option. If there are 10 different prizes on the first shelf, how many ways can you select your prizes?
30,240
Area codes for phone numbers are 3 digits long. How many different area codes can be made from the digits 0 through 9 if no digit is used more than once in any single area code?
720
In how many orders can 7 chapters be arranged in the index of a textbook if the chapter on probability is to be listed in the middle of the series of chapters?
720
In how many ways can 6 people be arranged in a line?
720
How many different batting orders are possible if 9 people are chosen from a group of 12 on a baseball team?
79,833,600
Which expression is used to evaluate 9C6?
9!/6!3!
A bag contains 12 pencils, 6 ball pens, and 2 sketch pens. Ronald takes out one writing object from this bag to note down some important information. What is the probability that a ball pen or a pencil is selected?
9/10
What is the probability of selecting a vowel or a letter from the word random? Hint: Determine if events happen at the same time.
9/26✔️
The Lindbergh High School carnival has a raffle for one trip to a theme park. The number of students buying raffle tickets in each class is given in the table below. Each student has a single ticket. What are the odds the raffle winner will be from the freshmen class?
9:37
Each player on the soccer team can choose a jersey from the team jersey set, and each jersey contains a different two-digit number from 10 to 99. Chris chooses 32, and then Pat chooses 77.
Dependent
A drawer contains 3 red paperclips, 4 green paperclips, and 5 blue paperclips. One paperclip is taken from the drawer and then replaced. Another paperclip is taken from the drawer. Explain why this is an independent or a dependent event.
Dependent - the sample space changes from the first event to the second event
For an in-class demonstration, a teacher draws a card from a freshly-shuffled deck. That card is a jack. The jack is not put back in the deck. A student states that the chance of drawing a king is now better than before. What, if anything, is incorrect about the student's logic?
The student's logic is correct; since drawing 2 cards from a deck is a dependent event, the probability of the second card being a king is better than the first card being a jack.
In a game show, cards are displayed showing different prizes. There are 10 cards showing a car, 10 cards showing a holiday trip, and 20 cards showing a house. If the host selects 6 cards in succession without replacement, what is the probability of getting 3 cards showing a car, followed by 2 cards showing a holiday trip, and finally, 1 card showing a house?
dependent; 30/63973
A bowl contains 3 red, 8 blue, and 7 black beads. Margaret randomly selects 3 beads one after the other without replacement. Find the probability of getting a red, blue, and black bead, in that order.
dependent; 7/204
Consider a fair 6 sided number cube, where each side has one number 1 - 6. All of the even faces are green and all of the odd faces are red. The probability of rolling the number cube and getting a 5 and a green face at the same time is an example of __________.
mutually exclusive events
If n is a positive integer, how does nPn comoare to nP(n-1)?🔸
nP(n-1) is n times greater.
Given the following circumstances, what counting formula should be used? 1) The order of selection is important. 2) Repetition is not allowed. 3) There are no identical objects.
nPr
A drawer contains 3 red socks, 4 white socks, and 2 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is blue and the second sock is red?
²/₂₇
red, then blue
³/₂₀
What is the probability of having 2 boys and 1 girl?
³/₈
P(2, red)
¹/₁₀
A new gourmet restaurant offers a choice of 4 main courses and 3 desserts. If you randomly choose a main course and a dessert, what is the probability of choosing the chef's favorite main course and dessert?
¹/₁₂
A standard six-sided number cube is rolled and a coin is tossed. What is the probability that the cube shows a 3 and the coin is tails?
¹/₁₂
To play a game, you spin a spinner and take a card. The spinner has equal sections that tell you to move 1, 2, 3 or 4 spaces. The cards read Free Turn, Lose a Turn, or No Change. Find the probability that you move 3 spaces and lose a turn.
¹/₁₂
Two standard number cubes are tossed. What is the probability of getting a 5 on the first number cube and an even number on the other?🔹
¹/₁₂
What is the probability that the first spinner will land on A, the second spinner will land on an even number, and the third spinner will land on Blue?
¹/₁₂
An experiment consists of tossing 2 fair coins, a dime and a quarter. Find the probability that both coins will land the same way.
¹/₂
As a part of a contest, a store is giving a special prize if a contestant can roll 3 standard six-sided number cubes, and get the same number on each. What is the probability a contestant will be successful?
¹/₂₁₆
A letter is chosen from the words BABY GIRL and then replaced. Find P(Y and R).
¹/₃₂
Jamie has three raffle tickets. One hundred tickets were sold. Her name was not drawn for the first prize. What is the probability that her name will be drawn for the second prize?
¹/₃₃
Jane buys a box of 50 donut holes. There are 8 coconut, 7 jelly, 10 honey-dipped, 10 chocolate, 9 powdered sugar, and 6 cinnamon donut holes in the box. Jane's favorite kind is chocolate and her second favorite kind is jelly. What is the probability that she will pick her two favorite kinds of donut holes in the order she likes them? After Jane chooses one, she does not put it back into the box.🔹
¹/₃₅
In a certain game, a player throws a standard 6-sided number cube twice per turn. What is the probability that the result of the first throw will be a 1, and the result of the second throw will be greater than 3?
¹/₃₆
What is the probability of rolling a 6 and then a 1 on consecutive rolls of a standard, 6-sided number cube?
¹/₃₆
Tamara likes to mix and match her 4 scarves, 3 pairs of gloves, and 2 hats. The colors are in the table On Monday, she randomly picks out a scarf, hat, and a pair of gloves. What is the probability of Tamara choosing a pair of black gloves and a red hat?
¹/₄
You toss a coin two times. Find the probability of getting heads on both tosses.
¹/₄
Franco has 7 quarters in his pocket. Of these, 3 depict the state of Delaware, 2 depict Georgia, 1 depicts Connecticut and 1 depicts Pennsylvania. Franco removes 1 quarter from his pocket and then removes a second quarter without replacing the first. What is the probability that both will be Delaware quarters?
¹/₇
Find P(heads, A).
¹/₈
A school cafeteria has 3 containers of white milk, 5 containers of chocolate milk and 2 containers of apple juice left. Iliana is first in line and Vishal is second. If the drinks are given out randomly, what is the probability that Iliana will get chocolate milk and Vishal will get apple juice?
¹/₉
P(Player 1 rock, Player 2 paper)
¹/₉
P(both scissors)
¹/₉
Bob has a set of 10 colored markers in a backpack. One is yellow and one is blue. What is the probability Bob will reach into the backpack without looking and grab the yellow marker and then reach in a second time and grab the blue marker?
¹/₉₀
On a multiple choice test, each question has five possible answers. A student does not know the answers to two questions, so he guesses. What is the probability that the student will get them both wrong?
¹⁶/₂₅
There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble?🔹
⁴/₁₅
What is the probability of choosing a red marble or a green marble out of a bag containing 5 blue marbles, 3 red marbles, and 1 green marble?
⁴/₉
A bag contains 5 chocolate, 3 peanut butter, 4 oatmeal and 4 sugar cookies. If 2 cookies are selected randomly, what is the probability that they will be the same kind?
⁵/₂₄
A letter is chosen from the words BABY BOY and then replaced. Find P(B and B).
⁹/₄₉
How many distinct committees of 6 people can be formed if the people are drawn from a pool of 17 people? Use factorials to express the answer.
₁₇C₆ = 17!/11!6!
How many different four-digit numbers can be made using the digits 1, 2, 3, 4, 5, 6 if no digit can be used more than once?
₆P₄ = 360
If a coin is flipped 75 times, in how many ways could there be exactly two tails?
₇₃C₂ = 2880
Which of the following best describes: P(each is a 25)
🚫1/26 🚫9/30 1/780 *145/156
A company makes two versions of a particular software product, a standard version and a deluxe version. Out of 25,000 units shipped, 5,000 were the deluxe version. As a part of a promotion, 1 product in every 500 contained a gift certificate. If a product is chosen at random, which is the probability it will be a standard version with a gift certificate?
🚫¹/₅₀ 🚫1/25,000
