Q.9 Shaquille O’ Neal is a 60% career free throw shooter, 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

Shaquille O’Neal’s career free throw percentage is approximately 60% in this problem context.
When modeling 10 independent free throw attempts, the situation follows a
binomial distribution with success probability p = 0.6.
The probability of making exactly 6 shots is calculated using the binomial formula.

Binomial Formula Basics

The binomial probability formula is:

Where:

• n = 10 (number of trials)
• k = 6 (number of successes)
• p = 0.6 (probability of success)

Substituting values:

C(10, 6) = 210
0.6⁶ ≈ 0.046656
0.4⁴ = 0.0256

P(6) = 210 × 0.046656 × 0.0256 = 0.2508

Correct Answer Breakdown

This result matches the exact binomial probability for independent Bernoulli trials.
The value is highest near the mean np = 6, which is expected behavior
for a binomial distribution.

Why Other Options Are Wrong

(B) 0.2816
Slightly higher than the correct value; may result from rounding errors or using
p ≠ 0.6.

(C) 0.2934
Too large; possibly obtained using a normal approximation or incorrect value of k.

(D) 0.6000
Represents only the single-shot success probability and ignores the binomial framework.