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?