Question

A basketball player has a 70% free throw percentage. Which plan could be used to simulate the number of free throws she will make in her next five free throw attempts?

I. Let 0,1 represent making the first shot and 2,3 represent making the second shot.....8,9 represent making the fifth shot. Generate five random numbers 0-9 ignoring repeats
II. Let 0,1,2 represent missing a shot and 3,4....,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9
III. Let 0,1,2 represent missing a shot and 3,4....,9 represent making a shot. Generate five random numbers 0-9 and count how many numbers are in 3-9, ignoring repeats

a. I only
b. II only
c. III only
d. II and III
e I, II, and III

Answer 1

Only Plans II and III correctly simulate a basketball player's 70% free throw percentage by using the digits 0-2 for misses and 3-9 for makes over five attempts. Plan I incorrectly simulates the probability and is discarded.Option D is the correct answer.

Step-by-step explanation:

The question asks which plan could be used to simulate the number of free throws a basketball player, who has a 70% free throw percentage, will make in her next five free throw attempts.

Plan II and Plan III suggest the same method, where the digits 0, 1, and 2 represent a missed shot, and the digits 3-9 represent a made shot. Since the player has a 70% success rate, this ratio of success to failure correctly simulates the player's free throw percentage.

Option I is incorrect because assigning each shot to specific pairs of digits (e.g. 0,1 for the first shot, 2,3 for the second shot, and so on), disregarding repeats, does not reflect the 70% probability correctly. Generating five random numbers within the range and counting how many fall between 3 and 9, ignoring repeats, does not change the probability since the repeats are not relevant to the outcome of each individual shot.

Therefore, the correct answer is that both Plan II and Plan III could be used make the simulation, making the answer II and III which corresponds to option d.