If you throw exactly one head in three tosses of a coin you win $87. If not, you pay me $48. Enter the expected value of the proposition. Round your answer to two decimal places.
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Expert's answer
2012-08-14T09:58:10-0400
The number X of heads in three tosses of a coin has binomial distribution with
p=0.5, q=1-p=0.5 and n=3.
Then the expected value of the proposition is
E = 87 * P(X=1) + 48 *P(X<>1).
We have
P(X=1) = C_3^1 p q^2,
where C_3^1 = 3!/(1! 2!) = 6 / 2 = 3 is the binomial coefficient.
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