In a game, a player tosses $3$ fair coins. He wins $\$10$ if $3$ heads occur, $\$p$ if&

Question

In a game, a player tosses $3$ fair coins. He wins $\$10$ if $3$ heads occur, $\$p$ if $2$ heads occur, $\$3$ if $1$ head occurs and $\$2$ if no head occurs. Express in terms of $p$ his expected gain from each game. Given that he pays $\$4.50$ to play each game, calculate the value of $p$ for which the game is fair (the player will neither win or lose in the long run), and his expected gain or loss over $100$ games if $p= 4.90$.

Accepted Answer

Expected payout $\frac{21+3p}{8}$; (a) $p=5$; (b) expected loss $\$3.75$.

Discrete Random Variables (DRV) - Expected Payoffs and Fair Games

Discrete Random Variables (DRV) - Expected Payoffs and Fair Games

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