Discussion
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?
Answer: A
The probability is about 0.2508.
Each attempt succeeds with probability 0.6, independently, so the number of successes in 10 attempts is binomial:
\[ \begin{aligned} P(6) &= \binom{10}{6}(0.6)^{6}(0.4)^{4} \\ &= 210 \times 0.046656 \times 0.0256 \\ &\approx 0.2508 \end{aligned} \]
0.6000 is the success rate per attempt, not the chance of exactly 6 in 10. The other values come from errors in the binomial coefficient or the powers; even the most likely count of a binomial has probability well below 0.6.
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