if a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which…

if a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?\n$100\\left(\\frac{1}{500}\\right)+(-5)\\left(\\frac{499}{500}\\right)=e(x)$\n$95\\left(\\frac{1}{500}\\right)+(-5)\\left(\\frac{499}{500}\\right)=e(x)$\n$(100 - 5)\\left(\\frac{1}{500}\\right)=e(x)$\n$(100)\\left(\\frac{1}{500}\\right)=e(x)$

if a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?\n$100\\left(\\frac{1}{500}\\right)+(-5)\\left(\\frac{499}{500}\\right)=e(x)$\n$95\\left(\\frac{1}{500}\\right)+(-5)\\left(\\frac{499}{500}\\right)=e(x)$\n$(100 - 5)\\left(\\frac{1}{500}\\right)=e(x)$\n$(100)\\left(\\frac{1}{500}\\right)=e(x)$

Answer

Explanation:

Step1: Calculate net - gain for winning

The winning prize is $100 and the ticket cost is $5. So the net - gain for winning is $100 - 5=95$. The probability of winning is $\frac{1}{500}$ since there is 1 winning ticket out of 500 tickets.

Step2: Calculate net - gain for losing

If a person loses, they just lose the cost of the ticket, which is - 5 (negative because it's a loss). The probability of losing is $\frac{499}{500}$ since there are 499 non - winning tickets out of 500 tickets.

Step3: Use the expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}x_ip_i$, where $x_i$ are the possible values and $p_i$ are their corresponding probabilities. Here, $E(X)=95\times\frac{1}{500}+(- 5)\times\frac{499}{500}$.

Answer:

$95\left(\frac{1}{500}\right)+(-5)\left(\frac{499}{500}\right)=E(X)$