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?

Answer 1

Answer: It will take approximately 0.923 years for Claire to earn back her initial investment

Step-by-step explanation:

1. The expected value for the point guard taking a three-point shot can be calculated by multiplying the probability of making the shot (0.30) by the value of a successful three-point shot (3) and the probability of missing the shot (0.70) by the value of a missed shot (0).

Expected value for taking a three-point shot = (0.30 * 3) + (0.70 * 0) = 0.90

2. The expected value for the teammate taking a two-point shot can be calculated by multiplying the probability of making the shot (0.48) by the value of a successful two-point shot (2) and the probability of missing the shot (0.52) by the value of a missed shot (0).

The expected value for passing the ball and the teammate taking a two-point shot = (0.48 * 2) + (0.52 * 0) = 0.96

3. Based on the expected values, the teammate taking a two-point shot has a higher expected value (0.96) compared to the point guard taking a three-point shot (0.90). Therefore, the point guard should pass the ball to the teammate for a higher expected value.

4. For Claire's investment decision, we can calculate the expected value by multiplying each possible outcome (profit or loss) by its corresponding probability and summing the results.

Expected value = (0.2 * (-10000)) + (0.4 * 0) + (0.3 * 5000) + (0.1 * 8000)

Expected value = (-2000) + (0) + (1500) + (800)

Expected value = (-2000) + (1500) + (800)

Expected value = 1300

5. The expected value of Claire's investment is $1300. Since the expected value is positive, it suggests that Claire should invest in the new business.

6. To calculate the number of years it will take for Claire to earn back her initial investment of $1200, we can divide the initial investment by the annual expected value.

Number of years to earn back initial investment = $1200 / $1300

Number of years to earn back initial investment ≈ 0.923 years (approximately 0.923 years)