Question

Shaquille O' Neal is a 60% career free throw shoots, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

• A. 0.2508
• B. 0.2816
• C. 0.2934
• D. 0.6000

Answer 1

The correct option is A 0.2508

Let X = {No. of successful throws}

Given that, the probability of success,

$p=\frac{60}{100}=0.6$

$\therefore$ Probability of failure,

q = 1 - 0.6 = 0.4

$\therefore$ The probability that he will successfully make exactly 6 free throws in 10 attempts is given by

P(X = r success) $={}^n{C}_r{p}^r{q}^{n-r};$

(where, n = 10 and r = 6)

So, $P(X=6)={}^{10}{C}_6\left(0.6{)}^6\right(0.4{)}^{10-6}$

= 210 × 0.0467 × 0.0256
= 0.251