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Maria will take two books with her on a trip. Suppose that

A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross ISBN: 9780321794772 63

Solution for problem 12STE Chapter 3

A First Course in Probability | 9th Edition

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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross

A First Course in Probability | 9th Edition

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Problem 12STE

Problem 12STE

Maria will take two books with her on a trip. Suppose that the probability that she will like book 1 is .6, the probability that she will like book 2 is .5, and the probability that she will like both books is .4. Find the conditional probability that she will like book 2 given that she did not like book 1.

Step-by-Step Solution:
Step 1 of 3

Solution 12STE

Step1 of 2:

From the given problem we have:

The probability that Maria will like book 1 = 0.6,

The probability that Maria will like book 2 = 0.5, and

The probability that she will like both books = 0.4.

We need to find the conditional probability that she will like book 2 given that she did not like book 1.


Step2 of 2:

Let us consider an event ‘A’ be the event that Maria likes book 1 and B be the event that Maria likes book 2. Then, is the conditional probability that she will like book 2 given that she did not like book 1.

Consider,

   

Where,

                   

                       

               

Now,

                   

Therefore, the conditional probability that she will like book 2 given that she did not like book 1 is 0.25.


Step 2 of 3

Chapter 3, Problem 12STE is Solved
Step 3 of 3

Textbook: A First Course in Probability
Edition: 9
Author: Sheldon Ross
ISBN: 9780321794772

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Maria will take two books with her on a trip. Suppose that