Answer to Question #104787 in Statistics and Probability for M'zamo Buthelezi

Question

tennis player made a successful first serve 67% of the times. If she continues to serve at the same rate the next time she play
and serves 6 times in the first game, determine the probability that:
1.2.1. All six first serves will be in.
1.2.2. At least 4 first serves will be in.

Answer 1

It is a Binomial distribution problem with $P=0.67, n=6$

1.2.1 $P(=6)$

The Excel Binomial formula=BINOM.DIST(6,6,0.67,FALSE) yields 0.090458.

Answer: 0.090458

1.2.2 $P(\geq4)$

$P(\ge4)=1-P(\le3)$

From BINOM.DIST Excel formula; $P(\le3)$ is given by =BINOM.DIST(3,6,0.67,TRUE) which yields 0.313048

Thus, $P(\ge4)=1-0.313048=0.686952$