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vredina [299]
3 years ago
9

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?
Mathematics
1 answer:
Harman [31]3 years ago
7 0

Answer:

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) =

1 - 0.075 = 0.925

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.

E(X) = \displaystyle\sum x_i(P(x_i))\\E(x) = +5.50(0.075) + (-1)(0.925)\\E(x) = -0.5125

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

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