Question

A card is drawn from a standard​ 52-card deck. Calculate the expected value for the game. A player must pay 8 dollars to play the​ game, which must be subtracted from the winnings. If a club is​ drawn, the player wins 21 ​dollars; otherwise, they lose their 8 dollars. Calculate the price that would make the game fair.

Answer 1

P(club) = 13/52 = 1/4

So, P(win) = 1/4

P(loose) = 3/4

Hence, expected value is -$2.75.

This is showing that on an average player will loose $2.75 per game.

For the fair price:

Let the cost be 'x':

Then:

To be a fair game E(x) = 0

-x + 5.25 = 0

x = 5.25

So, the cost of $5.25 will make the game fair.

Please comment if any doubt. Thank you.