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# An excellent free-throw shooter attempts several free

## Problem 1E Chapter 2.5

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition

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Problem 1E

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-by-Step Solution:

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.

Step 3 of 3

##### ISBN: 9780321923271

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9th. The full step-by-step solution to problem: 1E from chapter: 2.5 was answered by Sieva Kozinsky, our top Statistics solution expert on 07/05/17, 04:50AM. This full solution covers the following key subjects: free, Probability, throw, misses, attempt. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The answer to “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?” is broken down into a number of easy to follow steps, and 59 words. Probability and Statistical Inference was written by Sieva Kozinsky and is associated to the ISBN: 9780321923271. Since the solution to 1E from 2.5 chapter was answered, more than 555 students have viewed the full step-by-step answer.

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