Question

question number 8. (10.00 points) suppose you want to play a carnival game that costs 9 dollars each time you play. if you win, you get $100. the probability of winning is 1/50. what is the expected value of the amount that you, the player, stand to gain? -7.00 -6.90 -2.00 -6.70 7.00 none of the above

Explanation:

Step1: Define gain in case of win

The gain when winning is the prize money minus the cost to play. So, if you win, the gain $G_{win}=100 - 9=91$ dollars. The probability of winning $P_{win}=\frac{1}{50}$.

Step2: Define gain in case of loss

The gain when losing is just the negative of the cost to play. So, $G_{loss}=- 9$ dollars. The probability of losing $P_{loss}=1 - \frac{1}{50}=\frac{49}{50}$.

Step3: Calculate expected - value

The formula for the expected value $E$ of a discrete - random variable is $E = P_{win}G_{win}+P_{loss}G_{loss}$.
Substitute the values:
\[

$$\begin{align*} E&=\frac{1}{50}\times91+\frac{49}{50}\times(-9)\\ &=\frac{91}{50}-\frac{49\times9}{50}\\ &=\frac{91 - 441}{50}\\ &=\frac{- 350}{50}\\ &=- 7 \end{align*}$$

\]

Answer:

-7.00