Statistics probability

Question

A basketball player estimates that he makes 72% of the free throws he takes. if he takes 9 shots, find the probability that he makes 1 of the nine shots. Round your answer to accurate to 4 decimal places.

Answer 1

Binomial distribution

p = probability of success = 0.72

q = probability of failure = 1 - p = 0.28

Probability of 1 of 9 shots

There are 9 C 1 = 9 ways of choosing the shot he makes (1st, 2nd, ... 3rd)

For each of these ways the probability is p q⁸ (He has 1 success and 8 failures)

So the required probability is p q⁸ 9 times, or 9 p q⁸

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On a TI-84 you can find this directly

2nd VARS

A (binompdf)

trials = 9 (9 shots)

p 0.72

x 1 (you are interested in 1 success)

Hit paste

2.448 x 10^-4 = 0.0002448

If you find 9pq⁸ you should get the same result