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

Respuesta :

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) = [tex]0.001[/tex]

So, P(lose) = [tex]1-0.001=0.999[/tex]

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?

               [tex]u = E(x) =[/tex]∑[tex]x\times P(x)[/tex]

                  [tex]= 499\times0.0001+ (-1)\times0.999[/tex]

                  = [tex]-0.50[/tex]

Here,

Standard deviation of the expected winnings

           [tex]V (X) =[/tex]  ∑[tex](x-u)^{2} \times P(x)[/tex]

                     =   ∑ [tex](499-(-0.50))^{2} \times 0.001 + (-1-(-0.50))^{2} \times 0.999[/tex]

                     [tex]= 249.75[/tex]

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

               SD(x) = [tex]\sqrt{249.75}[/tex]

                        ≅ $15.80

Hence

The expected value of profit is ≅ $15.80

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