Question

Calculate the expected return in a game where sam wins $1 with the probability of 1 3 , $5 with the probability of 1 6 , and $0 with the probability of 1 2
a. $0.
b. $1 1 6 .
c. $ 2 1 6 .
d. $3

Answer 1

The expected value of events $x_i$ with probabilities $p(x_i)$ is given by

$E(x)=\Sigma x_ip(x_i)$

Given that in a game, Sam wins $1 with the probability of $\frac{1}{3}$ , $5 with the probability of $\frac{1}{6}$ , and $0 with the probability of $\frac{1}{2}$

Sam's expected winnings is given by:

$E(x)=1\left( \frac{1}{3} \right)+5\left( \frac{1}{6} \right)+0\left( \frac{1}{2} \right) \\ \\ =\frac{1}{3}+\frac{5}{6}= \frac{7}{6} =1.17$

Therefore, Sam's expected winnings is $1.17