In the New York State Numbers Lottery, you pay $1 and can bet that the sum of the numbers that come up is 13. The probability of winning is 0.075, and if you win, you win $6.50, which is a profit of $5.50. If you lose, you lose $1. What is the expected value of your profit? Is it an expected gain or an expected loss?

The expected value of profit is -0.5125. This is expected loss as value is negative.        

Step-by-step explanation:

We are given the following in the question:

P(winning) = 0.075

Thus,

P(Loosing) =

If we win we gain a profit of $5.50 and if we loose the lottery, we loose $1.

Thus, we can form the probability distribution in the following manner:

  Event:      Winning       Loosing

Profit(x):      +5.50               -1

     P(x):       0.075             0.925

We have to calculate the expected value of the profit.

Thus, the expected value of profit is -0.5125. This is expected loss as value is negative.

answer:   x = 3 + √11     and     x = 3 - √11

step-by-step explanation:

x² - 6x + 9 = 11

(x - 3)² = 11

x - 3 = ±√11

    x = 3 ± √11

x = 3 + √11     and     x = 3 - √11

1/8 3/16 3/4

step-by-step explanation:

you put them as all the same denominator and multiply