Cognitive Reflection Test Cognitive Reflection Probability and Statistical Intuition 1 — Questions and Answers
Question 1: A disease affects 1 in 1,000 people. A test for it is 99% accurate. You test positive. What is the approximate probability you actually have the disease?
- About 99%
- About 50%
- About 9% (Correct answer)
- About 1%
Correct answer: About 9%
With only 1 in 1,000 people having the disease, most positives are false positives, making the true probability roughly 9%.
Question 2: A fair coin is flipped 5 times and lands heads each time. What is the probability the next flip is heads?
- Less than 50% — it's 'due' for tails
- More than 50% — heads is on a streak
- Exactly 50% (Correct answer)
- Cannot be determined
Correct answer: Exactly 50%
Each coin flip is independent, so the probability of heads is always 50% regardless of prior results.
Question 3: In a group of 23 people, what is the approximate probability that two share a birthday?
- About 5%
- About 25%
- About 50% (Correct answer)
- About 75%
Correct answer: About 50%
The Birthday Paradox shows that with just 23 people, there is approximately a 50% chance two share a birthday.
Question 4: If you flip a fair coin twice, what is the probability of getting at least one head?
- 25%
- 50%
- 75% (Correct answer)
- 100%
Correct answer: 75%
The only outcome without a head is TT (25%), so the probability of at least one head is 75%.
Question 5: A bag has 3 red and 7 blue marbles. You draw one without looking. What is the probability it is red?
- 3%
- 10%
- 30% (Correct answer)
- 70%
Correct answer: 30%
There are 3 red marbles out of 10 total, giving a probability of 3/10 = 30%.
Question 6: Two independent events each have a 50% probability of occurring. What is the probability BOTH occur?
- 100%
- 50%
- 25% (Correct answer)
- 10%
Correct answer: 25%
For independent events, multiply the probabilities: 0.5 × 0.5 = 0.25, or 25%.
Cognitive Reflection Test Cognitive Reflection Probability and Statistical Intuition 1
A disease affects 1 in 1,000 people.
A test for it is 99% accurate.
You test positive.
What is the approximate probability you actually have the disease?