Practice Probabilistic Thinking in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Probabilistic thinking is the habit of reasoning about uncertain outcomes in terms of likelihood, expected value, and distributions rather than certainties.

Instead of 'Will X happen?' ask 'How likely is X?' and plan for multiple outcomes.

Example 1

medium
A medical test is 95% accurate. You test positive. Should you conclude you have the disease? Calculate the probability you actually have it if the disease prevalence is 1%.

Example 2

hard
The Monty Hall Problem: 3 doors, prize behind 1. You pick door 1. Host opens door 3 (no prize). Should you switch to door 2? Calculate probabilities for staying vs. switching.

Example 3

easy
You roll a die and it shows 1, 2, 3, 4, 5 five times in a row (never 6). What is the probability of rolling a 6 on the next roll? Explain the correct probabilistic reasoning.

Example 4

hard
Risk framing effect: 'This surgery has a 90% survival rate' vs. 'This surgery has a 10% mortality rate.' Are these equivalent? Explain how framing affects decisions and what probabilistic thinking reveals.
← Back to Probabilistic Thinking Worked Examples