Example-1: A basketball player makes 80 percent of his free throws during the regular season. Consider his next eight free throws a. What is the probability that he will make at least six free throws?

Step 1 ：Given that the basketball player makes 80 percent of his free throws, we have p = 0.8 and n = 8.

Step 2 ：We need to find the probability of making at least 6 free throws, which means we need to calculate the probability of making exactly 6, 7, and 8 free throws and then sum them up.

Step 3 ：Using the binomial probability formula: P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Step 4 ：Calculate the probability of making exactly 6 free throws: \(P(X=6) = C(8, 6) * 0.8^6 * (1-0.8)^{(8-6)} \approx 0.2936\)

Step 5 ：Calculate the probability of making exactly 7 free throws: \(P(X=7) = C(8, 7) * 0.8^7 * (1-0.8)^{(8-7)} \approx 0.3355\)

Step 6 ：Calculate the probability of making exactly 8 free throws: \(P(X=8) = C(8, 8) * 0.8^8 * (1-0.8)^{(8-8)} \approx 0.1678\)

Step 7 ：Sum up the probabilities: \(P(X \geq 6) = P(X=6) + P(X=7) + P(X=8) \approx 0.2936 + 0.3355 + 0.1678 = 0.7969\)

Step 8 ：\(\boxed{\text{Final Answer: The probability that the basketball player will make at least six free throws in his next eight attempts is approximately 0.7969 or 79.69%}}\)