Question

A player tosses two fair coins. He wins $5 if 2 heads occur, $2 it 1 head occurs and $1 if no heads occur. () Find his expected to play the game if it is to be fair? winnings. ) How much should he pay

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Answer #1

From the given information, the following is the probabilty distribution

outcomes 0 head 1 head 2 heads
winning amount(x) 1 2 5
p (x) 0.25 0.5 0.25

i) Expected winnings = \sumX * P(X) = 1 * 0.25 + 2 * 0.5 + 5 * 0.25 = 2.5

ii) For fair Game, Expected value = 0

i.e  So if it is fair game he has pay $2.5, since it the expected return which is reversed amount

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