AP Stats Probability Practice

The distribution of colors of candies in a bag is shown in the table. If two candies are randomly drawn from the bag with replacement, what is the probability that they are the same color?

• 0.09

• 0.22

• 0.25

• 0.75

• 0.78

Which of the following graphs represents a binomial distribution with n = 20 and p = 0.25?

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Two college roommates have each committed to donating to charity each week for the next year. The roommates’ weekly incomes are independent of each other. Suppose the amount donated in a week by one roommate is approximately normal with mean $30 and standard deviation $10, and the amount donated in a week by the other roommate is approximately normal with mean $60 and standard deviation $20. Which of the following is closest to the expected number of weeks in a 52-week year that their combined donation will exceed $120 ?

• 0; the combined donation never exceeds $120 in a week

• 1 week

• 3 weeks

• 5 weeks

• 8 weeks

The probability of winning a certain game is 0.5. If at least 70 percent of the games in a series of n games are won, the player wins a prize. If the possible choices for n aren=10, n=20, and n=100, which value of n should the player choose in order to maximize the probability of winning a prize?

• n=10 only

• n=20 only

• n=100 only

• n=10 or n=20 only; the probabilities are the same.

• n=10 or n=20 or n=100 ; the probabilities are the same.

Every Thursday, Matt and Dave's Video Venture has "roll-the-dice" day. A customer may choose to roll two fair dice and rent a second movie for an amount (in cents) equal to the numbers uppermost on the dice, with the larger number first. For example, if the customer rolls a two and a four, a second movie may be rented for $0.42. If a two and two are rolled, a second movie may be rented for $0.22. Let X represent the amount paid for a second movie on roll-the-dice day. The expected value of X is $0.47 and the standard deviation of X is $0.15. If the customer rolls the dice and rents a second movie every Thursday for 20 consecutive weeks, what is the total amount that the customer would expect to pay for these second movies?

• $0.45

• $0.47

• $0.67

• $3.00

• $9.40

Each of the faces of a fair six-sided number cube is numbered with one of the numbers 1 through 6, with a different number appearing on each face. Two such number cubes will be tossed, and the sum of the numbers appearing on the faces that land up will be recorded. What is the probability that the sum will be 4, given that the sum is less than or equal to 6 ?

• 2/36

• 3/36

• 3/15

• 2/9

• 4/6

A contestant’s final winnings on a game show are determined by a random selection of a base amount and a possible multiplier. For the base amount, the contestant randomly selects one of four cards, where two cards are marked $1,000, one card is marked $2,000, and one card is marked $5,000. After choosing the card, the contestant randomly selects one of five chips, where three chips are red and two chips are white. If the selected chip is red, the contestant’s final winnings are twice the value of the base amount. If the selected chip is white, the contestant’s final winnings are the value of the base amount. What is the probability that a contestant’s final winnings are exactly $2,000?

• 0.100

• 0.200

• 0.250

• 0.325

• 0.400

The probability that a new microwave oven will stop working in less than 2 years is 0.05. The probability that a new microwave oven is damaged during delivery and stops working in less than 2 years is 0.04. The probability that a new microwave oven is damaged during delivery is 0.10. Given that a new microwave oven is damaged during delivery, what is the probability that it stops working in less than 2 years?

• 0.05

• 0.06

• 0.10

• 0.40

• 0.50

A fair coin is flipped 10 times and the number of heads is counted. This procedure of 10 coin flips is repeated 100 times and the results are placed in a frequency table. Which of the frequency tables below is most likely to contain the results from these 100 trials?

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An online customer service department estimates that about 15 percent of callers have to wait more than 8 minutes to have their calls answered by a person. The department conducted a simulation of 1,000 trials to estimate the probabilities that a certain number of callers out of the next 10 callers will have to wait more than 8 minutes to have their calls answered. The simulation is shown in the following histogram. Based on the simulation, what is the probability that at most 2 of the next 10 callers will have to wait more than 8 minutes to have their calls answered?

• 0.150

• 0.190

• 0.474

• 0.526

• 0.810