Chapter 13.5, Problem 22PPS

a.

To determine

To determine probability that a family vacations is in the mountains.

Answer to Problem 22PPS

  $P\left(A\right)=0.3$

Explanation of Solution

Given information:

  $\begin{array}{l}P\left(B\right)=0.6\\ P\left(B\cap M\right)=0.2\end{array}$

Probablity that family did not go either destination is 0.9

  

Probability that family gone for vacation is 1-0.1=0.9

  $P\left(B\right)=0.6$

Now we know that sum of all probability is 1.

Hence we get,

  $\begin{array}{l}P\left(A\right)+P\left(B\right)=0.9\\ P\left(A\right)+0.6=0.9\\ P\left(A\right)=0.3\end{array}$

b.

To determine

To determine probability that a family already visited beach will also visit mountain.

Answer to Problem 22PPS

  $P\left(B|M\right)=\frac{1}{3}$

Explanation of Solution

Given information:

  $\begin{array}{l}P\left(B\right)=0.6\\ P\left(B\cap M\right)=0.2\end{array}$

Probablity that family did not go either destination is 0.9

  

  $P\left(B\right)=0.6$

Here we have to find the value of $P\left(B|M\right)$

Now we know that,

  $P\left(B|M\right)=\frac{P\left(B\text{ and }M\right)}{P\left(M\right)}$

Now put the values we get,

  $P\left(B|M\right)=\frac{0.2}{0.6}=\frac{1}{3}$