The point guard of a basketball team has to make a decision about whether or not

Question

The point guard of a basketball team has to make a decision about whether or not to shoot a three-point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time.
Xi 3 0
P(xi) 0.30 0.70


Xi 2 0
P(xi) 0.48 0.52




What is the expected value for each choice?


Should he pass the ball or take the shot himself? Explain.



Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits.
Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values.




If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?

Explanation / Answer

Expected value of 3 point attempt = 3*0.30 + 0*0.70 = 0.9

Expected value of 2 point attempt = 2*0.48 + 0*0.52 = 0.96

Since the expected value of 2 point attempt is greater, he should pass the ball.

Expected value of investment = -10000*0.2 + 0*0.4 + 5000*0.3 + 8000*0.1

                                           = -2000+1500+800

                                           = 300

Since the expected value shows profit, she should invest in the new business.

If the expected value stays constant, then 4 years will be taken to earn back 1200, because 1200/300=4

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