You toss a coin three times. If you toss heads exactly two times, you win $2. If you toss heads all three times, you win $8. Otherwise, you lose $3. What is the expected payout for one round of this game? Round your answer to the nearest cent. Enter an expected loss as a negative number

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Chica

16 September, 06:43

You toss a coin three times. If you toss heads exactly two times, you win $2. If you toss heads all three times, you win $8. Otherwise, you lose $3. What is the expected payout for one round of this game? Round your answer to the nearest cent. Enter an expected loss as a negative number

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Answers (1)

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Nigel Farmer · Answer 1

-0.75

Explanation:

We will examine the sample space, which is used in games like this one, to see the possible outcomes of the game:

H H H

H H T

H T H

T H H

T T H

T H T

H T T

T T T

The probability for getting three heads is 1/8. The probability for getting two heads is 3/8. And the probability for everything else is 1/2.

So, when the probabilities and the payouts (or losses) are put in the weighted formula, we get:

1/8*8 + 3/8*2 + 1/2 * (-3) = - 0.75

So the expected loss in the game is 0.75 dollars.