00:01
In this exercise, we are told that a tennis player, a certain tennis player, can serve successfully 70 % of the time.
00:09
And we are also told that we can assume that each serve is independent of the others.
00:14
So that means that we can view these serves as bernoulli trials, where each trial is independent of the others.
00:21
And for each trial, we can define success and failure.
00:25
So we'll call success getting the serve in from the question we're told the probability of that is 70%.
00:31
And in the question now we're told that she's going to serve six times.
00:39
So we have six trials.
00:44
Now if we define x as the number of serves that she gets in, we can say that x is a binomial random variable based on six trials and probability of success of 0 .7.
01:11
For part a we're asked what is the probability that she gets all six serves in? so recall that the probability mass function for our a binomial random variable is given as follows.
01:41
So the probability that x is equal to 6.
01:44
Using this formula, it simplifies to, well, it's just six successes, so it's 0 .7 to the exponent 6, which comes out to 0 .118.
02:01
So she has almost a 12 % chance of getting all 6 serves in.
02:08
For b, we are asked the probability that she gets exactly four serves in.
02:12
So using our probability mass function, which comes out to 0 .34...