Answer: Expected Value = -0.31
We expect to lose about 31 cents each time we play the game.
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Step-by-step explanation:
A = event of selecting a king
B = event of not selecting a king
P(A) = 4/52 since there are 4 kings out of 52 total. This fraction reduces to 1/13.
P(B) = 48/52 = 12/13
Note: P(A) + P(B) = 1.
V(A) = net value of selecting a king
V(A) = 100-8 = 92, so you net $92 if event A occurs.
V(B) = -8, meaning you lose 8 dollars if you select anything but a king
We multiply the probability values with their corresponding net values
P(A)*V(A) = (1/13)*(92) = 7.07692 approximately
P(B)*V(B) = (12/13)*(-8) = -7.38462 approximately
Add up the results:
7.07692 + (-7.38462) = -0.3077
The expected value is approximately -0.3077 which rounds to -0.31
We expect to lose on average 31 cents each time we play the game. The nonzero expected value means this is not a mathematically fair game.