Question

You are in a basketball 3-point contest. You have 1 regular ball, and 1 money ball left to shoot. If you make

both shots, you will get a total of 10 points. If you make just the money ball, you will get 3 points. Under
any other outcome, you will receive 0 points.
You approximate that the probability of you making the regular shot is 60% and the probability of you
making the money ball is 70%. You assume that each shot is independent.
What is the expected number of points you will score?

Answer 1

The expected number of points you will score in the basketball 3-point contest is 4.74.

Step-by-step explanation:

To find the expected number of points you will score, we need to calculate the expected value.

The expected value is the sum of the products of each possible outcome and its corresponding probability.

Let X be the number of points you will score, which can take on three values: 0, 3, or 10.

The probabilities for each outcome are as follows:

• P(X = 0) = P(missing both shots) = (1 - 0.6) * (1 - 0.7) = 0.4 * 0.3 = 0.12
• P(X = 3) = P(making only the money ball) = 0.6 * (1 - 0.7) = 0.6 * 0.3 = 0.18
• P(X = 10) = P(making both shots) = 0.6 * 0.7 = 0.42

Now we can calculate the expected value:

E(X) = 0 * P(X = 0) + 3 * P(X = 3) + 10 * P(X = 10)

E(X) = 0 * 0.12 + 3 * 0.18 + 10 * 0.42 = 0 + 0.54 + 4.2 = 4.74

Therefore, the expected number of points you will score is 4.74.