Suppose that you are considering whether to invest in a new business that a frie

Question

Suppose that you are considering whether to invest in a new business that a friend of yours is starting. After researching the possibilities, you decide that you will gain $40,000 if the business is successful, and you will lose $10,000 if the business is not successful.

a.) Suppose that 30% of all such businesses are successful, so you consider .3 to be the probability that your friend’s business will be successful. Determine the expected value of your net profit. (Here and always, show your method of solution.)

b.) Write a sentence interpreting/explaining what this expected value means, as if to a college student who has never taken a probability and statistics class.

c.) If you decide to invest in your friend’s business, what is the probability that your net profit will exceed its expected value?

Explanation / Answer

a) p = 0.3

q = 1 - 0.3 = 0.7

Expected value = 40000 * 0.3 - 10000 * 0.7

EV = 12000 - 7000 = 5000

b) Expected value is the mean or average money that we will get if we invest in the business.

c) EV lies close to 50%

So, P = 1/2

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