SOLUTION: A card is drawn from a standard​ 52-card deck. Calculate the expected value for the game. A player must pay 5 dollars to play the​ game, which must be subtracted from t

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Question 1131743: A card is drawn from a standard​ 52-card deck. Calculate the expected value for the game. A player must pay 5 dollars to play the​ game, which must be subtracted from the winnings. If a
spade is​ drawn, the player wins 15 ​dollars; otherwise, they lose their 5 dollars. Calculate the price that would make the game fair.
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


P(spade) = 1/4; P(not spade) = 3/4.

Value (spade) = $10 (-$5 for playing, +$15 for winning)
Value (not spade) = -$5

Expected value of playing: %281%2F4%29%2810%29%2B%283%2F4%29%28-5%29+=+10%2F4-15%2F4+=+-5%2F4

The expected value of playing the game is -$1.25.

To make the game fair (make the expected value of playing equal to 0), the cost for playing the game should be x, where

%281%2F4%29%2815-x%29%2B%283%2F4%29%28-x%29+=+0
15%2F4-%281%2F4%29x+-+%283%2F4%29x+=+0
15%2F4-x+=+0
x+=+15%2F4+=+3.75

ANSWER: The price for playing the game, to make the game fair, should be $3.75.