Question

Jane is playing a game in which he spins a spinner with 6 equal-sized slices numbered 1 through 6. The spinner stops on a numbered slice at random This game is this: Jane spins the spinner once. She wins $1 if the spinner stops on the number 1, $4 if the spinner stops on the number 2, $7 if the spinner stops on the number 3, and $10 if the spinner stops on the number 4. She loses $8.75 if the spinner stops on 5 or 6.
Find the expected value of playing the game.

Answer 1

Answer:

The expected value of playing the game is $0.75.

Step-by-step explanation:

The expected value of a random variable is the weighted average of the random variable.

The formula to compute the expected value of a random variable X is:

$E(X)=\sum x\cdot P(X=x)$

The random variable X in this case can be defined as the amount won in playing the game.

The probability distribution of X is as follows:

Number on spinner:   1           2           3          4           5              6

Amount earned (X):   $1        $4         $7        $10     -$8.75     -$8.75

Probability:                 1/6       1/6         1/6        1/6         1/6           1/6

Compute the expected value of X as follows:

$E(X)=\sum x\cdot P(X=x)$

         $=(1\times \frac{1}{6})+(4\times \frac{1}{6})+(7\times \frac{1}{6})+(10\times \frac{1}{6})+(-8.75\times \frac{1}{6})+(-8.75\times \frac{1}{6})$

         $=\frac{1}{6}+\frac{4}{6}+\frac{7}{6}+\frac{10}{6}-\frac{8.75}{6}-\frac{8.75}{6}$

         $=\frac{1+4+7+10-8.75-8.75}{6}$

         $=0.75$

Thus, the expected value of playing the game is $0.75.