Question

question number 7. (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 the carnival stands to gain? o 4.00 o 1.00 o -4.00 o 3.90 o 3.80 o none of the above

Explanation:

Step1: Define gain values and probabilities

The carnival stand gains $5$ dollars when the player loses (probability of losing is $1 - \frac{1}{100}=\frac{99}{100}$). When the player wins, the stand loses $100 - 5=95$ dollars (probability of winning is $\frac{1}{100}$).

Step2: Use expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}x_ip_i$. Here, $x_1 = 5$ (gain when player loses) with $p_1=\frac{99}{100}$, and $x_2=- 95$ (loss when player wins) with $p_2=\frac{1}{100}$. So, $E(X)=5\times\frac{99}{100}+(-95)\times\frac{1}{100}$.

Step3: Calculate the expected value

$E(X)=\frac{5\times99 - 95}{100}=\frac{495 - 95}{100}=\frac{400}{100}=4$.

Answer:

4.00