A player tosses two fair coins. He wins $5 if 2 heads occur, $2 if 1head occurs and $1 if no heads occur. (i) Find his expected winnings. (ii) How much should he pay to play the game if it is to be fair?
In case of a player tosses two fair coins then following events will occur:
S = [HT, TH, TT, HH]
(i) Expected winnings
"Expected-gain = \\Sigma X_i P(X_i )"
"=(5\\times\\frac{1}{4})+(2\\times\\frac{1}{2})+(1\\times\\frac{1}{4})"
"=\\frac{5}{4}+1+\\frac{1}{4}=\\frac{10}{4}=2.5"
(ii) Required pay to play the game
The player should pay exactly $2.5 if he wants to be fair in the game. It is because if he will pay less than $2.5 then the game is favorable to him, while unfavorable in case of pay more than.
Comments
Leave a comment