game is played by spinning a wheel that contains the words Win and Lose. The wheel has 10 slots, with Win written four times and Lose written six times. If the wheel lands on win, you win $5; on lose, you win nothing. It costs $2 to play. What is the expected value?
Answers
Given : game is played by spinning a wheel that contains the words
Win and Lose. The wheel has 10 slots, with Win written four times and Lose written six times.
If the wheel lands on win, you win $5;
on lose, you win nothing.
It costs $2 to play.
To Find : What is the expected value
Solution:
Win written four times and Lose written six times.
P (W) = 4/10 = 0.4
P (L) = 6/10 = 0.6
x net p(x) xP(x)
Win 5 - 2 = 3 0.4 1.2
Loose 0 - 2 = -2 0.6 -1.2
∑xP(x) = 1.2 - 1.2 = 0
Hence expected value of profit or loss is ZERO
or You can say expected value is 2 $ against 2$ cost
5(0.4) + 0(0.6) = 2 against 2 $ ticket.
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