Question

a basketball player makes 85% of her foul shots. if 10 of her foul shots are randomly selected, what is the probability that 8 of them are successful shots?
0.06
0.28
0.85
0.98

Explanation:

Step1: Identify the binomial probability formula

The binomial probability formula is \(P(X = k)=C(n,k)\times p^{k}\times(1 - p)^{n - k}\), where \(n\) is the number of trials, \(k\) is the number of successes, \(p\) is the probability of success on a single trial, and \(C(n,k)=\frac{n!}{k!(n - k)!}\)

Step2: Determine the values of \(n\), \(k\), and \(p\)

Here, \(n = 10\) (number of foul - shots), \(k = 8\) (number of successful shots), \(p=0.85\) (probability of making a foul - shot), and \(1 - p = 0.15\)

Step3: Calculate the combination \(C(n,k)\)

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Step4: Calculate \(p^{k}\) and \((1 - p)^{n - k}\)

\(p^{k}=(0.85)^{8}\approx0.2725\), \((1 - p)^{n - k}=(0.15)^{2}=0.0225\)

Step5: Calculate the probability \(P(X = 8)\)

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Answer:

B. \(0.28\)