In the New York State number lottery, you pay $1 and pick a number from 000-999. If your number comes up, you win $500, which is a profit of $499. If you lose you lose $1. Your probability of winning is 0.001. What is the expected value of your profit

Expected value of profit is ≅ $15.80

Step-by-step explanation:

from the Question,

Let the variable X represents the expected value of profit. X is called as random variable because picking a number from 000-999 digits is a Random process.

P(win) =

So, P(lose) =

Suppose that,

we really want to win this lottery. so we can go to the store and spend $1000 to buy all ticket (from 000 - 999). This would ensure your winning of $500 with one of the tickets (for a $499 profit), but the other 999 would be  losers (for a $999 loss).

What would be your average winnings on a per-ticket basis?

               ∑

                  =

Here,

Standard deviation of the expected winnings

             ∑

                     =   ∑

Taking square root of the variance to get the standard deviation:

               SD(x) =

                        ≅ $15.80

Hence

The expected value of profit is ≅ $15.80

the answer is b