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.

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.