Question

If the basketball player takes 8 independent free throws, with a probability of 0.7 of getting a basket on each shot, what is the probability that she gets exactly 6 baskets?

Answer 1

Let X denote number of getting baskets in n=8 independent free throws, with a probability p=0.7 of getting a basket on each shot. X has a binomial distribution Binomial (n=8, p=0.7).

The probability that she gets exactly 6 baskets is

$$P(X=6)=\dbinom{8}{6}*{0.7}^6*(1-0.7)^{8-6}$$ $$P(X=6)=\dfrac{8!}{6!(8-6)!}*0.7^6*0.3^2=0.296475$$