An excellent free-throw shooter attempts several free throws until she misses.

(a) If p = 0.9 is her probability of making a free throw, what is the probability of having the first miss on the 13th attempt or later?

(b) If she continues shooting until she misses three, what is the probability that the third miss occurs on the 30th attempt?

Step 1 of 3:

Here the experiment given is of a shooter who attempts several free throws until her first miss.

Let us denote a random variable X as the number of free attempts until the first miss.

Step 2 of 3:

(a)

Given that the probability of first miss p=09.We have to find the probability of first miss on 13th attempt or after that.

Here we can observe that random variable X follows geometric distribution with p=(1-0.9). That is X~geometric distribution with p=0.1.

The probability mass function o0f geometric distribution is given by,

P(X=x)=*p

Now we will find the probability of first miss on or after 13th attempt.It is given by,

P(X=13)=*0.1

=*0.1

=(0.28243)*(0.1)

=0.02824

Therefore the probability of first miss on or after 13th attempt is 0.02824.