Question

In a lottery, you pay $1 and pick a number from 000 to 999. If your number comes up, you win $350, which is a profit of $349. If you lose, you lose $1. Your probability of winning is 0.001. What is the expected value of your profit

Answer 1

Answer:

The expected value of profit is -$0.65.

Step-by-step explanation:

The rules of the lottery are as follows:

• You pay $1 and pick a number from 000 to 999.
• If your number comes up, you win $350, which is a profit of $349.
• If you lose, you lose $1.

The probability of winning is, P (W) = 0.001.

Then the probability of losing will be,

P (L) = 1 - P (W)

       = 1 - 0.001

       = 0.999

Let the random variable X represent the amount of profit.

The probability distribution table of the lottery result is as follows:

Result      X        P (X)

Win      +349     0.001

Lose         -1       0.999

The formula to compute the expected value of X is:

$E(X)=\sum X\cdot P(X)$

Compute the expected value of profit  as follows:

$E(X)=\sum X\cdot P(X)$

         $=(349\times 0.001)+(-1\times 0.999)\\\\=0.349-0.999\\\\=-0.65$

Thus, the expected value of profit is -$0.65.