Q 01/05

How many people in a room are needed before a shared birthday between two of them is more likely than not?

A) 23

B) 57

C) 183

D) 366

Answer · why

A) 23

Just 23 people are enough, because every pair in the room is a separate chance at a match and a group that size holds hundreds of pairs. Most people g...

Q 02/05

In the Monty Hall problem, what chance of winning the car does switching give once the host reveals a goat?

A) 1/2

B) 1/3

C) 2/3

D) 3/4

Answer · why

C) 2/3

Switching wins 2/3 of the time, because it loses only when the first pick was already the car, a one-in-three event. Pigeons trained on the puzzle lea...

Q 03/05

What do statisticians call the belief that a fair coin, after ten heads in a row, is 'due' to land tails?

A) Hot-hand fallacy

B) Sunk-cost fallacy

C) Base-rate fallacy

D) Gambler's fallacy

Answer · why

D) Gambler's fallacy

It is the gambler's fallacy, also called the Monte Carlo fallacy, and it runs backwards: past flips leave no trace on a fair coin, so tails stays at e...

Q 04/05

How many riffle shuffles did Bayer and Diaconis show a 52-card deck needs before its order is effectively random?

A) 7

B) 12

C) 20

D) 52

Answer · why

A) 7

Seven riffle shuffles is the finding of the 1992 Bayer–Diaconis paper, which showed a deck is nowhere near random after five and essentially perfect a...

Q 05/05

Roughly how many different orderings can a shuffled 52-card deck take, the number mathematicians write as 52 factorial?

A) About 8 × 10^15

B) About 8 × 10^33

C) About 8 × 10^67

D) About 8 × 10^120

Answer · why

C) About 8 × 10^67

A 52-card deck has 52! ≈ 8 × 10^67 orderings, so any properly shuffled deck is almost certainly in an order no deck in history has ever been in before...