# Answer to Question #13017 in Statistics and Probability for Stephanie

Question #13017

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.

Expert's answer

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.

Hence

P(X=1) = 3 * 0.5 * 0.5^2

= 3/8

Therefore

P(X<>1) = 1-P(X=1) = 1-3/8 =

5/8.

Therefore

E = 87 * P(X=1) + 48 *P(X<>1)

=

= 87 * 3/8 + 48 * 5/8 =

= 62.625

~ 62.63.

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.

Hence

P(X=1) = 3 * 0.5 * 0.5^2

= 3/8

Therefore

P(X<>1) = 1-P(X=1) = 1-3/8 =

5/8.

Therefore

E = 87 * P(X=1) + 48 *P(X<>1)

=

= 87 * 3/8 + 48 * 5/8 =

= 62.625

~ 62.63.

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