Answer
$0.23$
Work Step by Step
Define the events
$A_{1}$ = "Terrorism activities increase." $\quad P(A_{1})=0.3$ (three in ten chance)
$A_{2}$ = "Terrorism activities do not increase." $\quad P(A_{2})=1-0.3=0.7$
$B$ = "War breaks out"
The text gives $P(B|A_{1})=0.65$ and $P(B|A_{2})=0.05.$
We can now apply the theorem
$$\begin{align*}
P(B)&=\displaystyle \sum_{i=1}^{n}P(B|A_{i})P(A_{i}) & & \\
&= 0.65\cdot 0.3+0.05\cdot 0.7 \\
& =0.23 \end{align*}$$
