The host of a TV show offers you a choice of five closed boxes. One contains $1 000, one contains $500, one contains $100, and two are empty. He offers, for a price, to remove one of the empty boxes and let you choose among the remaining four. How much is this offer worth?
A)It's not worth anything, because you still might choose the other empty box.
B)$80
C)$320
D)$400
E)$1 600

Question

Quizplus · Accepted Answer

Initially, the expected value of choosing a box is calculated by adding the values of all boxes and dividing by the total number of boxes: (1000 + 500 + 100 + 0 + 0) / 5 = 320. After removing an empty box, the expected value becomes (1000 + 500 + 100 + 0) / 4 = 400. The difference, which represents the value of the offer, is 400 - 320 = 80.

The Host of a TV Show Offers You a Choice