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

Answer:

0.25 is the required probability.

Step-by-step 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:

$P(2|1') = \dfrac{P(2\cap 1')}{P(1')} = \dfrac{P(2)-P(1\cap 2)}{1-P(1)}\\\\P(2|1') =\dfrac{0.5-0.4}{1-0.6} = 0.25$

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