Question

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

Answer 1

Answer:

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) = $0.001$

So, P(lose) = $1-0.001=0.999$

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?

               $u = E(x) =$∑$x\times P(x)$

                  $= 499\times0.0001+ (-1)\times0.999$

                  = $-0.50$

Here,

Standard deviation of the expected winnings

           $V (X) =$  ∑$(x-u)^{2} \times P(x)$

                     =   ∑ $(499-(-0.50))^{2} \times 0.001 + (-1-(-0.50))^{2} \times 0.999$

                     $= 249.75$

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

               SD(x) = $\sqrt{249.75}$

                        ≅ $15.80

Hence

The expected value of profit is ≅ $15.80