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The expected value of the game is the mean value of the game
The expected value of the game is $1
<h3>How to determine the expected value?</h3>There are 13 spades in a deck of card of 52
So, the probability of selecting a spade is:
P(Spade) = 13/52
Simplify
P(Spade) = 1/4
Winning = $7
The probability of not selecting a spade is:
P(Not spade) = 1 - 1/4
Simplify
P(Not spade) = 3/4
Lose = $1
The expected value of the game is:
This gives
Simplify
Evaluate
Hence, the expected value of the game is $1
Read more about expected values at:
==> 7x - 4 = 3 + 8x
==> 8x - 7x = -4 - 3
==> x = -7 [ Ans ]