Question

A tennis player makes a successful first serve 77% of the time. If she serves 6 times what's the probability she gets: exactly 5 serves, at least 4 serves, no more than 4?

Answer 1

Question 24846A tennis player makes a successful first serve 77% of the time. If she serves 6 times what's the probability she gets: exactly 5 serves, at least 4 serves, no more than 4?

Solution. The number of successfull servings in the sequence of 6 serves has Binomial distribution with parameters $(6,0.77)$.

The probability that player gets exactly 5 successfull srves equals $\binom{6}{5}0.77^{5}0.23 \approx 0.37$, note that $\binom{6}{5} = 6$. The probability that player gets at least 4 serves equal $\sum_{i=4}^{6} \binom{6}{i} \cdot 0.77^i \cdot 0.23^{6-i} \approx 0.86$, here $\binom{6}{i} = \frac{6!}{(6-i)!i!}$ and the probability that the player gets no more than 4 equals $\sum_{i=0}^{4} \binom{6}{i} \cdot 0.77^i \cdot 0.23^{6-i} \approx 0.43$.