Cognitive Reflection Test Cognitive Reflection Probability and Statistical Intuition 2 — Questions and Answers
Question 1: A lottery ticket costs $2 and the jackpot is $10 million with odds of 1 in 20 million. What is the expected value of the ticket?
- $10 million
- $2.00
- $0.50 (Correct answer)
- -$1.50
Correct answer: $0.50
Expected value = ($10,000,000 / 20,000,000) = $0.50, which is less than the $2 cost.
Question 2: You roll a six-sided die. What is the probability of rolling a number greater than 4?
- 1/6
- 2/6 (1/3) (Correct answer)
- 3/6 (1/2)
- 4/6 (2/3)
Correct answer: 2/6 (1/3)
Only 5 and 6 are greater than 4, giving 2 out of 6 possible outcomes, or 1/3.
Question 3: If 80% of accidents happen within 15 miles of home, should you drive farther from home to be safer?
- Yes, driving farther reduces accident risk
- No, most driving occurs close to home (Correct answer)
- Only if you drive slowly
- Yes, highways are safer than local roads
Correct answer: No, most driving occurs close to home
Most driving happens close to home, so more accidents occur there due to exposure, not increased danger.
Question 4: A study shows that 90% of car accidents involve sober drivers. Does this mean drunk driving is safer?
- Yes, sober drivers cause more accidents
- No, sober drivers vastly outnumber drunk drivers on the road (Correct answer)
- Only on weekends
- The data is inconclusive
Correct answer: No, sober drivers vastly outnumber drunk drivers on the road
Because sober drivers make up the overwhelming majority of road users, they naturally account for more total accidents.
Question 5: You pick one card from a standard 52-card deck. What is the probability it is a face card (Jack, Queen, or King)?
- 3/52
- 12/52 (3/13) (Correct answer)
- 16/52 (4/13)
- 4/52
Correct answer: 12/52 (3/13)
There are 12 face cards (3 per suit × 4 suits) in a 52-card deck, giving a probability of 12/52 = 3/13.
Question 6: In a class of 30 students, 10 are left-handed. A student is chosen at random. What is the probability they are right-handed?
- 1/3
- 2/3 (Correct answer)
- 1/10
- 3/10
Correct answer: 2/3
20 out of 30 students are right-handed, giving a probability of 20/30 = 2/3.
Cognitive Reflection Test Cognitive Reflection Probability and Statistical Intuition 2
A lottery ticket costs $2 and the jackpot is $10 million with odds of 1 in 20 million.
What is the expected value of the ticket?