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

To calculate the expected return, multiply each amount that can be won by its corresponding probability, and sum these values. The expected return of the game is $1 1/6, which corresponds to answer choice (b).

Step-by-step explanation:

The student is asking how to calculate the expected return in a game with different probabilities of winning different amounts. To find the expected return, you multiply each outcome by its probability and then sum these products. The possible wins are $1, $5, and $0, with probabilities of 1/3, 1/6, and 1/2, respectively.

To calculate the expected return:

• For winning $1 with probability of 1/3: (1/3) × $1 = $1/3
• For winning $5 with probability of 1/6: (1/6) × $5 = $5/6
• For winning $0 with probability of 1/2: (1/2) × $0 = $0

Add up these expected values to get the total expected return:

$1/3 + $5/6 + $0 = $2/6 + $5/6 = $7/6

The expected return is $7/6, which simplifies to $1 1/6. Therefore, the correct answer is (b).

Answer 2

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
`(1)/(3)` , $5 with the probability of
`(1)/(6)` , and $0 with the probability of
`(1)/(2)`

Sam's expected winnings is given by:


`E(x)=1\left( (1)/(3) \right)+5\left( (1)/(6) \right)+0\left( (1)/(2) \right) \\ \\ =(1)/(3)+(5)/(6)= (7)/(6) =1.17`

Therefore, Sam's expected winnings is $1.17