2026

Mathematics & Logic

Test Probability Prowess: Nine Intriguing Scenarios

Nine medium-level puzzles await to probe your grasp of chance, risks, and statistical likelihoods in diverse settings.

#expected value#card draws#probability challenges#sampling without replacement#binomial odds#dice rolls#bayes theorem#conditional probability#medium math quiz

Quiz Intelligence

Total Questions

9

Difficulty Level

medium

Progress

0/0

0%

Quiz Questions

Answer all questions below and test your knowledge.

1
Two fair six-sided dice are rolled. What is the probability the sum is exactly 7?
Question 1
2
A family has two children. Given at least one is a boy, what is the probability both are boys?
Question 2
3
In the Monty Hall problem, you pick door 1, host opens door 3 (goat), should you switch to door 2?
Question 3
4
Expected value of a game: pay $2 to roll die, win $ (face value). Is it profitable?
Question 4
5
Binomial: 5 fair coin flips, probability exactly 3 heads?
Question 5
6
Deck of 52 cards, draw one. Probability it's a heart given it's red?
Question 6
7
Bayes: 1% disease prevalence, 99% accurate test. Positive test, probability have disease?
Question 7
8
Urn: 4 red, 6 black. Draw two without replacement. P both red?
Question 8
9
23 people in room, probability at least two share birthday (ignore leap)?
Question 9

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Test Probability Prowess: Nine Intriguing Scenarios

Quiz Intelligence

Quiz Questions

Two fair six-sided dice are rolled. What is the probability the sum is exactly 7?

A family has two children. Given at least one is a boy, what is the probability both are boys?

In the Monty Hall problem, you pick door 1, host opens door 3 (goat), should you switch to door 2?

Expected value of a game: pay $2 to roll die, win $ (face value). Is it profitable?

Binomial: 5 fair coin flips, probability exactly 3 heads?

Deck of 52 cards, draw one. Probability it's a heart given it's red?

Bayes: 1% disease prevalence, 99% accurate test. Positive test, probability have disease?

Urn: 4 red, 6 black. Draw two without replacement. P both red?

23 people in room, probability at least two share birthday (ignore leap)?