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.