Q.3.12 - A First Course in Probability

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 $1$. 

Step-by-Step Solution

Answer

The conditional probability is $0.25$.

Step 1: Given Information

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

Step 2: Explanation

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

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

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

Step 3: Final Answer

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