Question

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 $1$.

Short answer

The conditional probability is$0.25$.

Step-by-step solution

Given Information

Let $A$ be the event that Maria likes book land $B$ be the event that Maria likes book $2$. role="math" localid="1648005900157" $\mathrm{P}\left(B\mid {\mathrm{A}}^{\text{'}}\right)$ is the conditional probability that she will like book $2$ given that she did not like book $1$.

Explanation

$P\left(B\right|A^{\text{'}})$

$P\left(B{A}^{\text{'}}\right)=P\left(B\right)-P\left(BA\right)=0.5-0.4=0.1$

$P\left(B\mid A^{\text{'}}\right)=P\left(B{A}^{\text{'}}\right)/P\left(A\right)=0.1/0.4=0.25$

Final Answer 

$0.25$is the conditional probability that she will like book $2$given that she did not like book role="math" localid="1648006044624" $1$.