Probability

Question

If the probability that a certain tennis player will serve an ace is 1/4, what is the probability that he will serve exactly two aces out of 5 serves (assuming that the 5 serves are independent)?

 

 

 

 

 

Find P(Z < 1.45) for the standard normal variable Z corresponding the shaded area under the standard normal curve.

Answer 1

This is a binomial experiment.  We'll call an ace a success, and any either serve a failure. 

If we let p stand for the probability of a succes, then p = 1/4, and (1-p)=3/4.  (1-p) is the probability that he will NOT serve an ace, and is the complement of the event that he does serve an ace (thus mutually exclusive, satisfying a necessary condition of a binomial experiment).

 

The formula for the probability is

P (m successes in n trials) = (_nC_m)*p^m*(1-p)^(n-m).  _nC_m is a combination, read "n choose m".

 

We need to find the probability of obtaining 2 successes in 5 trials, so

P = (₅C₂)*(1/4)²*(3/4)³

 

= 10*3³/4⁵

=135/512