Question

question number 8. (10.00 points) suppose you want to play a carnival game that costs 5 dollars each time you play. if you win, you get $100. the probability of winning is 1/100. what is the expected value of the amount that you, the player, stand to gain? -4.00 -3.90 -1.00 4.00 -3.80 none of the above

Explanation:

Step1: Define gain values and probabilities

Let the gain when winning be $100 - 5=95$ (subtracting cost of play) with probability $p_1=\frac{1}{100}$, and the gain when losing be $- 5$ with probability $p_2 = 1-\frac{1}{100}=\frac{99}{100}$.

Step2: Use expected - value formula

The expected - value formula is $E(X)=\sum_{i}x_ip_i$. Here, $x_1 = 95$, $p_1=\frac{1}{100}$, $x_2=-5$, and $p_2=\frac{99}{100}$. So $E(X)=95\times\frac{1}{100}+(-5)\times\frac{99}{100}$.

Step3: Calculate the expected value

$E(X)=\frac{95 - 495}{100}=\frac{-400}{100}=- 4$.

Answer:

-4.00