Probability Reasoning

Probability Reasoning Difficulty 5 10 questions

Problems that test your intuition about chance, randomness, and conditional probability. Many of these have answers that feel wrong — but the math doesn't lie.

Instructions Calculate the probability and explain your reasoning. Show your work — a correct number without explanation earns partial credit. Fractions, decimals, or percentages are all accepted.

Question 1 of 10

A fair coin is flipped 5 times and comes up heads each time. What is the probability that the next flip will also be heads?

Question 2 of 10

A fair six-sided die is rolled. You are told the result is even.

Question 3 of 10

You roll two fair six-sided dice.

Question 4 of 10

You toss 3 fair coins.

Question 5 of 10

You draw one card from a standard 52-card deck.

Question 6 of 10

A bag contains 5 white marbles and 5 black marbles. You draw 2 marbles without replacement.

Question 7 of 10

A family has two children. You are told that at least one of them is a boy.

Question 8 of 10

You shuffle a standard 52-card deck and draw 2 cards without replacement.

Question 9 of 10

You choose one of three cards face down. One card is red on both sides, one is black on both sides, and one is red on one side and black on the other. You flip over your chosen card and see a red side. What is the probability the other side is also red?

Question 10 of 10

A disease affects 1% of a population. A test detects the disease 99% of the time when present (sensitivity), but gives a false positive 5% of the time when absent.

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