Question

ou are given 6 to 1 odds against tossing three heads with three coins, meaning you win $6 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game. Would you expect to win or lose money in 1 game? In 100 games? Explain.

Answer 1

Answer:

EV = $-0.125

For one game, the outcome cannot be predicted, even though you are more likely to lose money.

For 100 games, you are expected to lose about $12.50

Explanation:

Expected value is the sum of the product of all possible outcomes by their payouts. In this case, there are only 2 possible outcomes. You either win by tossing 3 three heads with three coins or lose.

The probability of winning (P(w)) is:

$P(w)=0.5*0.5*0.5\\P(h)=0.125$

Therefore, the probability of losing (P(l)) is:

$P(l)=1-0.125\\P(l)=0.875$

The expected value (EV) for the game is:

$EV= 6*0.125 - (1*0.875)\\EV = -0.125$

For one game, the outcome cannot be predicted, even though you are more likely to lose money than win. As for 100 games, since the expected value is negative, you are expected to lose money (about $12.50).