Chapter 9: Probability

1 / 495

Jessica is carrying eight pages of math homework and four pages of English homework. A gust of wind blows the pages out of her hands and she is only able to recover eight random pages. What is the probability that she recovers all of her math homework?

1/6

Mr. Martinez has 4 blue shirts, 6 white shirts, and 2 gray shirts. He will randomly choose a shirt to wear. What is the probability the shirt Mr. Martinez chooses will be gray?

9/21

Mr. Tindel will randomly choose a student from his class as the student council representative. There are 12 girls and 9 boys in his class. What is the probability Mr. Tindel will choose a boy?

2/15 (2/5 x 1/3 = 2/15)

Find the probability of spinning striped then A when you spin both spinners.

4/15 (2/5 x 2/3=4/15)

Find the probability of spinning striped then B when you spin both spinners.

1/15 (1/5 x 1/3=1/15)

Find the probability of spinning white then A when you spin both spinners.

1/8 (1/4 x 3/6=3/24)

Find the probability of spinning yellow and rolling an even number.

120 outcomes

Five books need to be placed on a shelf. You randomly arrange the books on the shelf from left to right. Find the number of possible outcomes in the sample space.

5/8

1 red marble, 3 green, 4 blue. What is the complement of picking a green? P(not green)

1/2

1 red marble, 3 green, 4 blue. What is the complement of picking a red or a green? P(not red or green)

7/8

1 red marble, 3 green, 4 blue. What is the probability of picking a green or blue?

8/15 (4/5 x 2/3=8/15)

Find the probability of spinning not white then B when you spin both spinners.

75%

A bag contains 3 red balloons, 2 purple balloons, 4 yellow balloons, 2 pink balloons, and 1 brown balloon. Without looking, Melissa pulls out a balloon. What is the probability Melissa pulls out a yellow, pink, or purple balloon? (As a percentage)

1 / 720

A chemistry lab requires students to identify chemical compounds by using various tests. Each student is given samples of three different compounds, labeled A, B, and C. Each student is also given a list of ten possible compounds. If a student does not perform the tests and randomly chooses three from the list, what is the probability that she guesses all three correctly?

1 / 126

A class has five boys and four girls. If the teacher randomly picks five students, what is the probability that he will pick all boys?

Tree Diagram

A device consisting of line segments;; shows all possibilities

1 / 35

A gambler places a bet on a horse race. To win, he must pick the top three finishers in any order. Seven horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win his bet?

1 / 462

A gardener has eleven identical-looking tulip bulbs, of which five will produce yellow tulips and six will become pink. She randomly selects and plants five of them and then gives the rest away. When the flowers start to bloom, what is the probability that all of them are yellow?

4 outcomes

A hot dog stand offers both small and large hot dogs. Each hot dog can be ordered plain or with mustard. Find the number of possible outcomes in the sample space.

1 / 84

A jar contains six black buttons and three brown buttons. If six buttons are picked at random, what is the probability that all of them are black?

19/30

A jar is filled with pennies, nickels, and dimes. The probability of picking a penny is 1/5, and the probability of picking a dime is 1/6 . What is the probability of picking a nickel?

108 outcomes

A jewelry store sells gold and platinum rings. Each ring is available in nine styles and is fitted with one of six gemstones. Find the number of possible outcomes in the sample space.

6 outcomes

A jewelry store sells gold and platinum rings. Each ring is fitted with a ruby, sapphire, or emerald gemstone. Find the number of possible outcomes in the sample space.

1024 outcomes

A math quiz has five multiple choice questions. Each question has four options: A, B, C, and D. Find the number of possible outcomes in the sample space.

1 / 55

A meeting takes place between a diplomat and eleven government officials. However, two of the officials are actually spies. If the diplomat gives secret information to nine of the attendees at random, what is the probability that no secret information was given to the spies?

1 / 21

A meeting takes place between a diplomat and seven government officials. However, two of the officials are actually spies. If the diplomat gives secret information to five of the attendees at random, what is the probability that no secret information was given to the spies?

1 / 210

A meeting takes place between a diplomat and ten government officials. However, four of the officials are actually spies. If the diplomat gives secret information to six of the attendees at random, what is the probability that no secret information was given to the spies?

1 / 20

A nature preserve has a population of five black bears. They have been tagged #1 through #5, so they can be observed over time. Two of them are randomly selected and captured for evaluation. One is tested for worms and one is tested for ticks. What is the probability that bear #3 is tested for worms and bear #5 is tested for ticks?

1 / 72

A nature preserve has a population of nine black bears. They have been tagged #1 through #9, so they can be observed over time. Two of them are randomly selected and captured for evaluation. One is tested for worms and one is tested for ticks. What is the probability that bear #3 is tested for worms and bear #5 is tested for ticks?

1 / 42

A nature preserve has a population of seven black bears. They have been tagged #1 through #7, so they can be observed over time. Two of them are randomly selected and captured for evaluation. One is tested for worms and one is tested for ticks. What is the probability that bear #3 is tested for worms and bear #5 is tested for ticks?

1 / 45

A nature preserve has a population of ten black bears. They have been tagged #1 through #10, so they can be observed over time. Two of them are randomly selected and captured for evaluation. What is the probability that bears #3 and #5 are captured for evaluation?

1 / 336

A politician is about to give a campaign speech and is holding a stack of eight cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack?

1 / 1320

A politician is about to give a campaign speech and is holding a stack of twelve cue cards, of which the first 3 are the most important. Just before the speech, she drops all of the cards and picks them up in a random order. What is the probability that cards #1, #2, and #3 are still in order on the top of the stack?

1 / 3003

A shipment of fifteen smartphones contains five with cracked screens. If sold in a random order, what is the probability that the first ten sold have undamaged screens?

12 outcomes

A spinner can land on either red or blue. You spin and then roll a six-sided die. Find the number of possible outcomes in the sample space.

1/12

A spinner has red, green, blue, and orange sections. The probability of landing on red is 3/4 , on green is 1/12 , on blue is 1/12. What is the probability of landing on an orange section?

1/3

Ana will spin the spinner below. What is the probability that Ana's spin will land on yellow?

Equally likely events

Events that have the same probability of occurring

1/10 (1/6 x 3/5=3/30)

Find the probability if you pick one marble, don't replace it, then pick a second marble: P(black, striped)

1/15 (1/6 x 2/5=2/30)

Find the probability if you pick one marble, don't replace it, then pick a second marble: P(black, white)

1/5 (3/6 x 2/5=6/30)

Find the probability if you pick one marble, don't replace it, then pick a second marble: P(striped, striped)

1/15 (2/6 x 1/5= 2/30)

Find the probability if you pick one marble, don't replace it, then pick a second marble: P(white black)

1/4 (3/6 x 3/6=9/36)

Find the probability if you pick one marble, replace it, then pick a second marble: P(striped, striped)

2/9 (2/6 x 4/6=8/36)

Find the probability if you pick one marble, replace it, then pick a second marble: P(white, not white)

1/6 (2/6 x 3/6=6/36)

Find the probability if you pick one marble, replace it, then pick a second marble: P(white, striped)

1/8 (3/4 x 1/6=3/24)

Find the probability of spinning and not getting blue and rolling 5.

1/24 (1/4 x 1/6=1/24)

Find the probability of spinning blue and rolling 2.

2/5 (3/5 x 2/3=2/5)

Find the probability of spinning not striped then B when you spin both spinners.

4/15 (4/5 x 1/3=4/15)

Find the probability of spinning not white then A when you spin both spinners.

57%

Of the water lilies in the pond, 43% are yellow. The others are white. A frog randomly jumps onto a lily. What is the probability that the frog jumped on a white lily? (As a percentage)

1/10 (1/4 x 2/5)

One letter is randomly selected from the word MATH, and a second letter is randomly selected from the work JOKES. What is the probability that both letters are vowels?

Theoretical Probability

Probability found by dividing the number of possible successful outcomes by the total number of possible outcomes. This probability does not require performing trials (like flipping a coin or rolling a die).

experimental probability

Probability found by running trials (like flipping a coin or rolling a die) and dividing the number of successful outcomes recorded by the total number of trials.

1/2

Terry placed 6 number tiles labeled 4, 7, 10, 11, 14, and 21 in a box. He will pick one of the number tiles from the box without looking. What is the probability Terry will pick a tile labeled with an odd number?

90 outcomes

The chess club must decide when and where to meet for a practice. The possible days are Tuesday, Wednesday, or Thursday. The possible times are 3, 4, or 5 p.m. There are ten classrooms available. Find the number of possible outcomes in the sample space.

Sample Space

The set of ALL possible outcomes of a probability experiment

1 / 70

There are eight songs on your playlist. Four of them are country and four are pop. With random shuffle and no repetition, you listen to four songs. What is the probability that you listened to all country songs?

1 / 1716

You've purchased a lottery ticket and your numbers are: 4-10-8. A lottery official randomly selects three balls from a set of thirteen balls that are numbered from #1 to #13. To win, your numbers must match the selected numbers in order. What is the probability of winning the lottery?

Probability Experiment

a situation involving chance that leads to results called outcomes

Compound event

at least two simple events

Event

one or more outcomes of an experiment

Dependent events

the first event does affect the possible outcomes for the second event

Independent events

the outcome of the first event does not affect the possible outcomes for the second event

Outcome

the result of a single performance or trial of an experiment