# Your friend is attempting 10 free throws, and from experience

Your friend is attempting 10 free throws, and from experience, you know that your friend’s probability of scoring a free throw is 0.7. What is the probability that your friend would score 8 free throws (ASSUME INDEPENDENCE)?

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Alix Ortiz

Step 1
The random variable X is defined as the number of free throws which follows binomial distribution with sample size 10 and probability of success is 0.7.
The binomial probability distribution is,
$$P(X=x)=\left(\begin{array}{c}n\\ x\end{array}\right)(p)^{x}(1-p)^{n-x}$$
In the formula, n denotes the number of trails, p denotes probability of success, and x denotes the number of success.
Step 2
The probability that would score 8 free throws is,
$$P(X=8)=\left(\begin{array}{c}10\\ 8\end{array}\right)(0.7)^{8}(1-0.7)^{10-8}$$
$$\displaystyle={45}\times{0.05764801}\times{0.09}$$
$$\displaystyle={0.2335}$$
Thus, the probability that would score 8 free throws is 0.2335.