Statistics · Practice

Probability — Exercises

Graded practice problems from foundations to advanced. Enter your answer and press Check.

Foundations

Problem 1

A fair coin is flipped. What is the probability of getting heads?

Problem 2

A fair six-sided die is rolled. What is the probability of rolling a $6$ ?

Problem 3

A fair die is rolled. What is the probability of rolling an even number?

Problem 4

Two fair coins are flipped. What is the probability of getting two heads?

Problem 5

Two fair coins are flipped. What is the probability of getting at least one head?

Problem 6

A die is rolled. $P(A) = 1/3$ , $P(B) = 1/2$ , $P(A \cap B) = 1/6$ .

Find $P(A \cup B)$ .

Problem 7

$P(A \cap B) = 0.2$ and $P(B) = 0.5$ . Find $P(A \mid B)$ .

Problem 8

Events $A$ and $B$ are independent. $P(A) = 0.5$ , $P(B) = 0.3$ . Find $P(A \mid B)$ .

Problem 9

Two cards are drawn without replacement from a 52-card deck. Find the probability both are aces.

Problem 10

In the birthday problem, how many people are needed for a greater-than-50% chance that at least two share a birthday?

Problem 11

$P(A) = 0.5$ , $P(B \mid A) = 0.8$ , $P(B \mid A^c) = 0.4$ .

Use Bayes' theorem to find $P(A \mid B)$ .