Probability Worksheet with Answers – AP Statistics (Free PDF)

Problem 1 Complement Rule ★★★

The probability that a package from a warehouse arrives late is 0.08. (a) Find the probability that a package arrives on time. (b) Two packages are sent independently. Find the probability that at least one is late.

Problem 2 Marginal Relative Frequencies ★★★

A school surveyed 250 students about membership in a sports club.

Find the marginal relative frequency of (a) club members, (b) 11th graders, (c) 9th graders.

Problem 3 Joint and Conditional Frequencies ★★★

Use the sports club table below.

Find (a) P(club member and Grade 10), (b) P(club member | Grade 11), (c) P(Grade 11 | club member).

Problem 4 Exclusive Events ★★★

At a lunch counter, 35% of customers order pizza and 25% order a sandwich, and no customer orders both. Find the probability that a customer orders pizza or a sandwich. Are the events independent?

Problem 5 Addition Rule with Overlap ★★★

For events A and B, P(A) = 0.52, P(B) = 0.31 and P(A and B) = 0.14.

Find P(A or B) and the probability of neither event.

Problem 6 Conditional Probability from Counts ★★★

Of 300 adults surveyed, 120 own an electric bike, 75 own a regular bike but no electric bike, and the rest own no bike. Among the electric bike owners, 90 also own a car. Find the probability that a randomly chosen electric bike owner owns a car, and the probability that a randomly chosen adult is an electric bike owner who owns a car.

Problem 7 Testing Independence with a Table ★★★

Among 200 students, 40 are left-handed and 160 are right-handed. Of the left-handed students, 12 wear glasses; of the right-handed students, 48 wear glasses. Are wearing glasses and handedness independent? Justify with probabilities.

Problem 8 Multiplication Rule for Free Throws ★★★

Mia makes 72% of her free throws, and shots are independent. Find the probability that (a) she makes her next three shots, (b) she misses the first and makes the next two.

Problem 9 Tree Diagram for Defects ★★★

Machine 1 makes 60% of a factory’s parts, with 3% defective. Machine 2 makes the other 40%, with 5% defective.

Find the probability that a randomly chosen part is defective.

Problem 10 Reverse Conditional Probability ★★★

A part from the factory in the previous problem is found to be defective. What is the probability that it came from Machine 1?

Problem 11 Designing a Simulation ★★★

A quiz has 4 multiple-choice questions, each with 5 options, and a student guesses every answer. Describe how to use random digits to simulate one quiz, then use these 8 simulated quizzes (each group of 4 digits is one quiz) to estimate the probability of getting at least 2 right: 4533 3147 8932 8804 0723 8625 5118 4873.

Problem 12 Using Simulation Results ★★★

A player’s set of five free throws was simulated 200 times. The graph shows the number of shots made in each trial.

Estimate the probability that the player makes at least 4 shots, and the probability that the player makes at most 2.

Problem 13 Finding a Missing Probability ★★★

Let X be the number of pets in a household: P(0) = 0.18, P(1) = 0.34, P(2) = 0.27, P(3) = k, P(4) = 0.06. Find k and P(X ≥ 2).

Problem 14 Mean of a Random Variable ★★★

Use the distribution of pets per household from the previous problem. Calculate the mean number of pets and interpret it.

Problem 15 Standard Deviation of a Random Variable ★★★

Calculate the standard deviation of the number of pets per household for the same distribution and interpret it.

Problem 16 Probability Histogram ★★★

The graph shows the probability distribution of the number of raffle tickets bought by a visitor.

Find P(X ≥ 4) and the mean number of tickets.

Problem 17 Expected Value of a Game ★★★

At a ring-toss booth, a player pays $3 to play. The prize is $0 with probability 0.7, $4 with probability 0.2 and $10 with probability 0.1. Find the expected net gain per play and interpret it.

Problem 18 Sampling without Replacement ★★★

A club has 250 members, 105 of whom are seniors. Two members are chosen at random without replacement for a committee. Find the probability that (a) both are seniors, (b) exactly one is a senior.

Problem 19 At Least One Success ★★★

Each customer entering a shop independently buys something with probability 0.15. Find the probability that among 5 customers (a) at least one buys, (b) the first buyer is the third customer.

Problem 20 Warranty Cost Distribution ★★★

A store sells a $40 extended warranty on a tablet. The repair cost X is $0 with probability 0.85, $120 with probability 0.09, $300 with probability 0.05 and $600 with probability 0.01. Find the mean and standard deviation of the repair cost, and the store’s expected profit per warranty.