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

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

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step-by-step explanation: