Question

Maria will take two books with her on a trip. Suppose that the probability that she will like book 1 is .6, the probabilitythatshewilllikebook2is .5,andtheprobability 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.

Answer 1

0.25 is the required probability.

Explanation:

We are given the following in the question:

Probability that like book 1 = 0.6

`P(1) = 0.6`

Probability that like book 2 = 0.5

`P(2) = 0.5`

Probability that Maria likes both the books = 0.4

`P(1\cap 2) = 0.4`

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

Thus, we have to evaluate:

`P(2|1') = (P(2\cap 1'))/(P(1')) = (P(2)-P(1\cap 2))/(1-P(1))\\\\P(2|1') =(0.5-0.4)/(1-0.6) = 0.25`

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