Concepts in Probability and Statistics - A
Nadine conducted an experiment with four possible outcomes. Trevor conducted the same experiment, but he doubled the number of trials. Which statements are true? Choose all that apply.
-Trevor has more experimental outcomes than Nadine. -Trevor's experimental probability is more likely closer to the theoretical probability than Nadine's.
Jason rolls a fair number cube labeled 1 through 6, and then he flips a coin. What is the probability that he rolls a 3 and flips a head?
1/12
A package contains 4 red, 2 green, 8 purple, and 6 blue jelly beans. What is the probability of choosing a purple jelly bean, eating it, and then choosing a blue jelly bean?
12/95
What is the probability of the complement of spinning an even number by using the spinner below?
5/8
Alina has a spinner that has 5 equal sections: red, blue, green, purple, and orange. She spins the spinner 200 times. About how many times should Alina expect the spinner to land on either purple or orange?
80
The probability of choosing a green grape out of the bag that contains red and green grapes without looking is mc002-1.jpg. Which term best describes this probability?
likely
The manager of a video game store found that 35 of the 140 people who preordered the latest baseball game canceled their orders the day before the game was released. He used that data to create a simulation to predict the probability that future customers will cancel their preorders. According to the manager's model, what is the probability that two customers who preorder the newest golf game will both cancel their orders the day before the game is released?
1/16
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown. mc011-1.jpg What is the probability of drawing a red marble out of the bag without looking?
1/3
How many different possible outcomes are there when Jillana spins the spinner below and then flips the coin?
12
A fair coin is tossed, and a marble is chosen from the bag whose contents are shown below. What is the probability of the coin landing heads up and a blue (B) marble being randomly selected?
3/20
Sixteen of the 24 schools in Ryan's county are public schools. Ryan used this spinner to predict the probability that the winner of the county spelling bee in each of the next four years will attend a private school. Which set of outcomes from Ryan's simulation implies that the winner will attend a private school at least three times in that span?
-B-B-A-B -A-B-B-B
Which situations can be simulated using this spinner? Check all that apply.
-Predicting the gender of a randomly chosen art teacher if 1 of 3 art teachers is female -Predicting the gender of a randomly chosen biology teacher if 8 of 12 biology teachers are female -Predicting the gender of a randomly chosen health teacher if 2 of 4 health teachers are female
What is the probability of an event that is impossible?
0
Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. About how many times should Kevin land on red or purple?
about 72 times
The spinner is divided into 8 equal sections. mc008-1.jpg Which two events have the same probability?
P(gray), P(green)
There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble?
(4/10+r)(r/10+r)
A six-sided number cube is labeled with the numbers 1-6, one number on each face. Each number is used exactly once. How many possible outcomes exist when the cube is rolled two times?
36
Lonnie threw 50 free throws and missed 16 of them. If Lonnie throws 75 free throws, what can be predicted about the number she will make successfully?
NOT Lonnie will make 24 free throws.
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown. mc014-1.jpg Which best describes the complement of choosing a red marble?
choosing a blue, green, or yellow marble
Michael practiced batting and kept track of his hits. He missed 2 balls but hit 8 balls that were pitched to him. How many balls can Michael predict to hit if he is pitched 20 balls?
16 balls
How many possible outcomes exist when Louisa spins the spinner below twice?
NOT 16
A spinner with 4 colors is spun for a total of 50 trials. Yellow was selected 10 times. What is the experimental probability of the spinner landing on yellow?
1/5
A tie rack contains 5 striped ties, 8 solid ties, and 6 polka dot ties. How many possible outcomes are there when choosing a tie from the rack?
19
A bag contains 5 red marbles, 3 green marbles, 2 purple marbles, 2 orange marbles, and 1 blue marble. mc023-1.jpg Which color marble is less likely to be picked than purple?
blue
Reese is using a coin to predict the gender of the puppies born to her dog. According to Reese's model, which is the probability that a litter of 5 puppies will be all males?
1/32
Elijah is going to spin a spinner 180 times. He predicts that 60 of those spins will result in the spinner landing on the section labeled 3. Based on the theoretical probability, which best describes Elijah's prediction?
jah's prediction is high because 180 x (1/4) = 45
Franz and his friends are using the spinners below to play a game. If one turn consists of spinning each spinner once, which table shows all the possible outcomes for one turn?
B
Four students each flip a coin multiple times and record the number of times the coin lands heads up. The results are shown in the table. Which student is most likely to find that the actual number of times his or her coin lands heads up most closely matches the predicted number of heads-up landings?
Collin
Hannah spins a spinner once and then randomly selects a marble from a bag. A representation of the spinner and the bag of marbles is shown below. She determines that the probability of spinning a multiple of 3 and randomly selecting a blue (B) marble is mc020-3.jpg. Which best describes the accuracy of Hannah's answer?
Hannah's answer is accurate.
Jonas is conducting an experiment using a 10-sided die. He determines that the theoretical probability of rolling a 3 is mc015-1.jpg. He rolls the die 20 times. Four of those rolls result in a 3. Which adjustment can Jonas make to his experiment so the theoretical and experimental probabilities are likely to be closer?
He can increase the number of trials.
The tree diagram below shows all of the possible outcomes for flipping three coins. What is the probability that at least two of the coins will be tails?
NOT 3/8
During an experiment, Juan rolled a six-sided number cube 18 times. The number two occurred four times. Juan claimed the experimental probability of rolling a two was approximately mc010-1.jpg. Why is Juan's experimental probability incorrect?
Juan used the number two in the numerator instead of the occurrences of the number two.
A restaurant owner has found that 80% of her customers return to the restaurant within two weeks. She wants to create a tool that will simulate the habits of her customers and allow her to predict the probability that three of the next four customers to visit her restaurant will return within two weeks. Which spinner simulation uses an appropriate device and has the correct number of trials?
a spinner divided into 5 congruent sectors, spun 4 times
Camila flips a fair coin two times and then spins a four-section spinner. How many possible outcomes exist?
16
Yuto has a bag containing 3 red marbles, 5 blue marbles, 2 green marbles, and 8 yellow marbles. Rin reaches into the bag, pulls out a blue marble, and puts it in her pocket. Then Misaki reaches in and pulls out a marble. What is the total number of possible outcomes for Misaki's marble?
17
A spinner is divided into 8 equal sections, and each section contains a number from 1 to 8. What is the probability of the spinner landing on a number that is greater than 5?
3/8
The tree diagram below shows all of the possible outcomes for flipping three coins. What is the probability of one of the coins landing on tails and two of them landing on heads?
3/8
The table below shows all of the possible outcomes for rolling two six-sided number cubes. What is the probability of rolling a sum of 8?
5/36
A three-section spinner, shown below, is spun twice. The tree diagram shows the possible outcomes for the two spins. What is the probability of spinning the same number in both spins?
1/3
A bag of marbles contains 4 green marbles, 3 blue marbles, 2 red marbles, and 5 yellow marbles. How many possible outcomes are there when choosing a marble from the bag?
14
Lola tossed a coin twice. She made a tree diagram to show the possible outcomes. Which tree diagram shows the sample space for two tosses of a coin?
A
Jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is mc016-1.jpg. The theoretical probability of rolling a 2 is mc016-2.jpg. What could Jamie do to make his experimental results more closely match the theoretical probability?
He can increase the number of trials.
Selena is buying an audio system for her car. She can choose among 3 types of stereos, 4 kinds of speakers, and 2 kinds of amplifiers. Which describes how Selena can show her options?
List the 3 types of stereos. Draw branches from each type and list the 4 speakers at the ends. Then, draw branches from each speaker type and list the 2 amplifiers at the ends.
The theoretical probability of an event occurring is mc003-1.jpg. Which best describes the experimental probability associated with this event?
Out of every 5 trials, the desired outcome will occur approximately 2 times.
Prisha rolls a fair number cube multiple times and records the result of each roll. Her results are shown in the table. How does the experimental probability of rolling a 3 compare with the theoretical probability of rolling a 3?
The experimental probability of rolling a 3 is 1/30 greater than the theoretical probability of rolling a 3.
Which best describes the complement of spinning any number less than 3?
spinning a 3 or 4
A shape is picked at random from the group below. mr022-1.jpg Which event has a theoretical probability of exactly mr022-2.jpg? Check all that apply.
-not picking a square -picking a shape that has only straight edges
The list below shows all of the possible outcomes for flipping four coins. What is the probability of at least two coins landing on heads?
11/16
A set of cards contains cards numbered 1 - 8. Mrs. Jacob's class is conducting an experiment in which a card is drawn from the pile, the number is recorded, and then the card is returned to the set. The class will conduct 1,000 trials. Based on the theoretical probability, which is the best prediction for the number of times a 4 will be drawn from the pile?
125
Marnie conducted an experiment using a bag of 12 marbles containing an equal number of blue, red, and green marbles. She randomly chose one marble, noted the color, and returned the marble to the bag. Marnie did this for a total of 20 trials. The table below shows the results. What was the experimental probability of choosing a blue marble from a bag?
7/20
Jason practiced making soccer goals and kept track of the results. He missed 3 goals but made 9 in one practice session. What can Jason predict regarding goals made if his next practice session has 24 tries?
Jason will make 18 goals.
How many possible outcomes exist when two fair coins are flipped and a three-section spinner is spun?
NOT 6
The experimental probability of getting a 6 on a number cube is mc001-1.jpg. Which is true about the event's experimental probability?
The number 6 came up 7 times out of a total of 40 trials.
A pizzeria makes pizzas in different sizes and with different toppings. The pizzeria wants its customers to have 12 options when they create a pizza. Which combination of size and toppings will give customers 12 options? Check all that apply.
-4 sizes and 3 toppings -2 sizes and 6 toppings -3 sizes and 4 toppings
What is the probability of the spinner landing on 2?
1/4
Two spinners that have sections numbered 1 through 5 are spun at the same time. Then, the numbers are added together. What is the total number of possible sums?
9
Frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin. He spun a 4 five times. Which statements are true? Choose all that apply.
NOT -For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased. -If the number of trials is changed, the experimental probability also changes. -If the number of trials is changed, the number of experimental outcomes also changes.
A set of face cards contains 4 Jacks, 4 Queens, and 4 Kings. Carlie chooses a card from the set, records the type of card, and then replaces the card. She repeats this procedure a total of 60 times. Her results are shown in the table. How does the experimental probability of choosing a Queen compare with the theoretical probability of choosing a Queen?
NOT The experimental probability is 1/15 more than the theoretical probability.
The 7 a.m. flight from Dallas to Chicago is on time 75% of the time. Fran created this spinner to simulate the scenario. Fran spun the spinner three times to predict whether the flight will be on time or late next Monday, Tuesday, and Wednesday. How should she interpret this outcome of the three spins: shaded-shaded-unshaded?
The flight will be late on one of the three days.
Jamie made the tree diagram below to show the different choices he has for ordering a pizza for lunch. According to the tree diagram, which best describes how many choices Jamie has for his pizza?
three choices for size, two choices for crust, and two choices for topping
Marlon asks a friend to think of a number from 5 to 11. What is the probability that Marlon's friend will think of the number 9?
1/7
A coin is tossed, and a four-section spinner is spun once. The tree diagram shows the possible outcomes for the two events. What is the probability of flipping tails on the coin and spinning a 2 on the spinner?
1/8
A box contains cards that are numbered from 1 to 100. What is the probability of randomly selecting a number that is less than 12?
11/100
A restaurant is offering a dinner special that includes one starter and one entree. The choices are listed below. Starter: breadsticks, soup, salad Entree: beef, fish, chicken, shrimp, pork How many possible dinner special combinations are there?
15
Vinay constructed this spinner based on the population of teachers at his school. According to Vinay's model, what is the probability that he will have a male history teacher two years in a row?
(3/8)^2
Cameron flips two coins and then spins the spinner below. What is the probability of having two different outcomes on the coins and spinning an odd number?
1/4
There were 3 apple, 1 mixed fruit, 2 grape, and 4 tropical fruit juice boxes in the cooler at the picnic. What is the probability that, when Jill reaches into the cooler to grab two juice boxes without replacing them, she grabs two that are grape?
1/45
A bag contains 15 marbles. The probability of randomly selecting a green marble is mc018-1.jpg. The probability of randomly selecting a green marble, replacing it, and then randomly selecting a red marble is mc018-2.jpg. What is the probability of randomly selecting a red marble?
1/5
A producer of electronic book readers is performing a quality check to ensure the reader's backlight is working correctly. The plant manager tests 2,000 readers on Monday and finds that 8 have defective backlights. The fraction es024-1.jpg is the experimental probability of a book reader having a defective backlight. What is the value of x?
250
Evelyn has a bag containing red (R), blue (B), and green (G) marbles as shown below. If each marble is replaced after it is drawn, what is the probability of randomly drawing three consecutive red (R) marbles?
27/512
Jalen is buying a new car. He has the options below. Model: compact, luxury, sport Transmission: automatic, manual Color: red, blue, black, yellow Jalen decides that he wants a yellow car. What is the total number of choices he has?
6
Tyler believes that an 8-sided die can be used to predict whether customers at his store will use a coupon when making their purchases, with a roll of 1 indicating a coupon and all other outcomes indicating no coupon. Today, 4 of the first 48 customers in the store used a coupon. How does the experimental probability of a customer using a coupon compare to the theoretical probability of Tyler's die?
NOT The experimental probability is less than the theoretical probability, but within 2%.
Luis rolled a number cube 60 times. He rolled the number 6 four times. Which is most likely the cause of the discrepancy between Luis's experimental outcome and the predicted outcome?
He did not perform enough trials.
Gerald is conducting an experiment with 3 possible outcomes. Kasey is conducting an experiment with 20 possible outcomes. Which statement best relates the sample space to the number of trials needed to produce results similar to their predicted outcomes?
NOT Gerald will need to conduct more trials because he needs to make up for the difference in the number of possible outcomes.
Shana lives in a town with a population of 130,000. Standing outside the largest grocery store, Shana surveyed people to find out how many have cats. Of the people she asked, 106 people had cats and 694 did not. How many cat owners are predicted to live in the town?
There should be 17,225 cat owners in town.
Mai conducted an experiment by flipping a fair coin 200 times. The coin landed heads up 110 times. Which statement about the coin landing heads up in Mai's experiment is correct?
The experimental probability of the coin landing heads up is 11/20 and the theoretical probability of the coin landing heads up is 1/2.
Ava surveyed the students in her homeroom about their footwear. She found that 12 students were wearing sneakers, 4 students were wearing boots, and 6 students were wearing dress shoes. She used this data to create a tool that would predict the footwear of randomly chosen students in the school. She placed 2 blue marbles, 3 red marbles, and 6 yellow marbles in a bag, and selected one marble, with replacement, for each student. What is the predicted footwear of three randomly chosen students if Ava drew two yellow marbles and 1 blue marble?
2 students wearing sneakers and 1 student wearing boots
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not replacing it, and then choosing a red marble?
1/12
Margaret is playing a game with a standard deck of 52 cards which contains 4 jacks. The first player to select a jack gets to start the game. What is the theoretical probability that Margaret, when choosing first, will choose a jack?
1/13
The table below shows all of the possible outcomes for rolling two six-sided number cubes. How many possible outcomes are there?
36
Which events have a probability of 25 percent? Check all that apply.
-choosing a green jelly bean out of a bag that contains 2 green jelly beans, 1 red jelly bean, and 5 yellow jelly beans -spinning a number less than 2 on a spinner that has four equal sections numbered from 1 to 4 -choosing a spade out of a standard deck of cards that contains 13 hearts, 13 clubs, 13 diamonds, and 13 spades
Theo is using this spinner to predict the favorite movie genre of randomly chosen students in his school. If Theo spins the spinner 60 times, how many times should he expect it to land on "Action"?
15
A bag of marbles contains 6 blue marbles, 2 yellow marbles, 4 red marbles, and 1 green marble. What is the probability of reaching into the bag and selecting a yellow marble?
2/13
Terry has a number cube that is numbered from 1 to 6. She rolls the cube 50 times. Which equation can be used to predict the number of times that she will roll a number that is greater than 4?
2/6(50)
Marissa is choosing a four-digit PIN for her ATM card. The first digit must be a digit from 1 through 9. For the other three digits, she can choose any combination of digits 0 through 9, but may not repeat a digit. Which shows part of the sample space for Marissa's PIN?
2345, 2034, 2134
Marcus performed an experiment by spinning a spinner a set number of times and noting the color on which the spinner landed. The table below shows the results. What is the experimental probability for the lowest frequency?
3/18
Which value cannot represent the probability of an event occurring?
3/2
A bag contains 15 marbles. The probability of randomly selecting a green marble is mc019-1.jpg. The probability of randomly selecting a green marble, replacing it, and then randomly selecting a blue marble is mc019-2.jpg. How many blue marbles are in the bag?
6
Three marbles, one red (R), one yellow (Y), and one blue (B), are placed in a bag. A fair coin is flipped, and then a marble is drawn out of the bag at random. A tree diagram of the events is shown below. How many possible outcomes exist?
6
Twelve of the last 16 winners of the school science fair have been seventh grade students. Mona placed 3 red marbles and 1 green marble in a bag to create a simulation to predict whether future science fair winners will be seventh graders. According to Mona's model, what is the probability that the next 4 winners will all be seventh grade students?
81/256
The students at Southern Junior High School are divided into four homerooms. Benjamin just moved into the school district and will be randomly assigned to one homeroom.
NOT -Use a random number generator with 1, 2, and 12 representing the first homeroom, 7, 9, and 10 representing the second homeroom, 3, 8, and 11 representing the third homeroom, and 4, 5, and 6 representing the fourth homeroom. -Spin a spinner with 8 congruent sections with 2 sections assigned to each homeroom.
A bag contains 1 red tile, 1 blue tile, 1 green tile, 1 yellow tile, and 1 purple tile. Kaison chooses a tile from the bag, records its color, and then replaces the tile. She repeats this procedure a total of 50 times. Her results are shown in the table. How does the experimental probability of choosing a yellow tile compare with the theoretical probability of choosing a yellow tile?
The experimental probability is the same as the theoretical probability.
James conducted an experiment with 4 possible outcomes. He determined that the experimental probability of event A happening is 10 out of 50. The theoretical probability of event A happening is 1 out of 4. Which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer?
completing the experiment many more times and combining the results to the trials already done
The spinner is divided into 10 equal sections. mr023-1.jpg Which event has theoretical probability of exactly mr023-2.jpg? Check all that apply.
-spinning a number less than 3 -spinning a 4 or 5 -spinning a number greater than 8
Juanita rolls a number cube x times. For which value of x are the experimental probability and the theoretical probability most likely to be equivalent?
1,000
April and Sanjay are both using tools to simulate the probability that a family with three children will have exactly one girl. April is using a coin, with tails up representing a boy and heads up representing a girl. She flipped the coin three times. Sanjay rolled a number cube three times with odd numbers representing a boy and even numbers representing a girl. Which statement best describes their simulations?
Both simulations have the same theoretical probability of a 3-child family having exactly one girl, but their experimental probabilities may differ.
Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is 7, Hannah wins. If the sum is not 7, Corrine wins. Corrine says Hannah can win only if the following occurs: 1 on the first cube, 6 on the second cube 2 on the first cube, 5 on the second cube 3 on the first cube, 4 on the second cube Which best explains if Corrine is correct?
Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.
Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins the spinner 180 times. Kevin determines about how many times the spinner will land on red or green, and his work is shown below. mc020-1.jpg What mistake did Kevin make, if any?
NOT Kevin calculated the prediction correctly and did not make any mistakes.
A set of face cards contains 4 Jacks, 4 Queens, and 4 Kings. Carlie chooses a card from the set, records the type of card, and then replaces the card. She repeats this procedure a total of 60 times. Her results are shown in the table. How does the experimental probability of choosing a Queen compare with the theoretical probability of choosing a Queen?
NOT The experimental probability is 1/15 more than the theoretical probability.
Twelve of the 20 students in Mr. Skinner's class brought lunch from home. Fourteen of the 21 students in Ms. Cho's class brought lunch from home. Siloni is using two 15-section spinners to simulate randomly selecting students from each class and predicting whether they brought lunch from home or will buy lunch in the cafeteria. If each spinner is divided into 15 congruent sectors, how does the spinner representing Mr. Skinner's class differ from the spinner representing Ms. Cho's class?
One fewer sector of the Skinner-class spinner will represent bringing lunch from home.
Which statement best describes the use of a simulation to predict the probability that two randomly chosen people will both have their birthdays on a Monday?
Randomly generate an integer from 1 to 7 two times, and the probability is 1/7^2.
Maria has an 8-sided die that is numbered from 1 to 8. She rolls the die 96 times. About how many times can she expect to roll an 8?
about 12 times