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:

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