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?\n100(\\frac{1}{500})+(-5)(\\frac{499}{500}) = e(x)\n95(\\frac{1}{500})+(-5)(\\frac{499}{500}) = e(x)\n(100 - 5)(\\frac{1}{500}) = e(x)\n(100)(\\frac{1}{500}) = 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?\n100(\\frac{1}{500})+(-5)(\\frac{499}{500}) = e(x)\n95(\\frac{1}{500})+(-5)(\\frac{499}{500}) = e(x)\n(100 - 5)(\\frac{1}{500}) = e(x)\n(100)(\\frac{1}{500}) = e(x)

Answer

Explanation:

Step1: Define winning and losing scenarios

The probability of winning is $\frac{1}{500}$ (since there is 1 winning - ticket out of 500). The net gain when winning is the prize money minus the cost of the ticket, which is $100 - 5=95$. The probability of losing is $\frac{499}{500}$, and the net gain when losing is $- 5$ (the cost of the ticket).

Step2: 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. So, $E(X)=95\times\frac{1}{500}+(-5)\times\frac{499}{500}$.

Answer:

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