Question

e is a game where the outcome is a random integer from 1 to 50. If the outcome is odd, you win If the outcome is even, you win nothing. If you play the game, what is the expected payoff?

Answer 1

total possible outcomes: 50

odd outcomes: 25

even outcomes: 25

probability of an odd outcome = 25/50 = 1/2

probability of an even outcome = 25/50 = 1/2

return in case of an odd outcome = $26

return in case of an even outcome = $0

The expected payoff is computed as follows:

`\begin{gathered} \text{ expected payoff=}p_(odd)\cdot r_(odd)+p_(even)\cdot r_(even) \\ \text{ expected payoff=}(1)/(2)\cdot26+(1)/(2)\cdot0 \\ \text{ expected payoff= \$13} \end{gathered}`