Cognitive Reflection Test Cognitive Reflection Probability and Statistical Intuition 2

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?

Accepted Answer

$0.50

Answer

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?

Accepted Answer

2/6 (1/3)

Answer

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?

Accepted Answer

No, most driving occurs close to home

Answer

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?

Accepted Answer

No, sober drivers vastly outnumber drunk drivers on the road

Answer

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)?

Accepted Answer

12/52 (3/13)

Answer

There are 12 face cards (3 per suit × 4 suits) in a 52-card deck, giving a probability of 12/52 = 3/13.

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