Question

A basketball player is practicing shooting free throws. Suppose she makes 75% of her free throw attempts. Make a tree diagram and probability model for what might happen if she decides to shoot three free throws. In other words, what is the probability that she makes zero shots, one shot, two shots, or all three shots.

MATCH YOUR SHOTS MADE WITH THE PROBABILITY
Column A Column B
0 shots made a) 14.2%
1 shot made b) 42.2%
2 shots made c) 4.8%
3 shots made d) 1.7%

Answer 1

Using binomial probability calculations, a basketball player making 75% of her free throws has a 1.6% chance to miss all three, a 14.1% chance to make one, a 42.2% chance to make two, and a 42.2% chance to make all three shots.

Step-by-step explanation:

A basketball player making 75% of her free throw attempts is trying to shoot three free throws. To calculate the probabilities of her making 0, 1, 2, or 3 shots, we can use a tree diagram or direct probability calculations with the binomial formula.

The probabilities for making ('M') or missing ('N') a free throw can be determined as follows:

Probability of making a shot (P): 0.75

Probability of missing a shot (1 - P): 0.25

The probabilities for different outcomes over three shots are:

0 shots made: NNN = (0.25)^3 = 0.015625 or 1.6%

1 shot made: MNN + NMN + NNM = 3 * (0.75) * (0.25)^2 = 0.140625 or 14.1%

2 shots made: MMN + MNM + NMM = 3 * (0.75)^2 * (0.25) = 0.421875 or 42.2%

3 shots made: MMM = (0.75)^3 = 0.421875 or 42.2%

Matching these probabilities with Column B, we get:

0 shots made: d) 1.7%

1 shot made: a) 14.2%

2 shots made: b) 42.2%

3 shots made: c) 4.8%