In a TV game show, four prizes are hidden on a game board which contains 80 spaces. One prize is worth $4,000, two prizes are worth $2,000, and the other prize is worth $100. The remaining spaces contain no prizes. The game show host offers a sure prize of $100 not to play this game. Should the contestant choose the sure prize or play the game?
A) doesn't matter
B) play
C) don't play

Question

In a TV game show, four prizes are hidden on a game board which contains 80 spaces. One prize is worth $4,000, two prizes are worth $2,000, and the other prize is worth $100. The remaining spaces contain no prizes. The game show host offers a sure prize of $100 not to play this game. Should the contestant choose the sure prize or play the game? ​
A) doesn't matter
B) play
C) don't play

Quizplus · Accepted Answer

There are 4 total prizes worth a total of $8,100. There are 76 blank spaces on the game board. Therefore, the probability of winning any prize is 4/80 or 1/20.

The expected value of playing the game can be calculated as:
(1/20 x $4000) + (2/20 x $2000) + (1/20 x $100) = $500

This means that, on average, a contestant can expect to win $500 by playing the game. Therefore, it would be more advantageous for the contestant to play the game and try to win one of the prizes rather than accepting the sure prize of $100.

In a TV Game Show, Four Prizes Are Hidden on a Game