Answer
$0.70$
Work Step by Step
Define the events
$A_{1}$ = "The person interviewed was a man." $\quad P(A_{1})=0.47$ (given)
$A_{2}$ = "The person interviewed was not a man." $\quad P(A_{2})=1-0.47=0.53$
$B$ = "The person interviewed answered truthfully."
The text gives $P(B|A_{1})=0.78$ and $P(B|A_{1})=0.63.$
We can now apply the theorem
$$\begin{align*}
P(B)&=\displaystyle \sum_{i=1}^{n}P(B|A_{i})P(A_{i}) & & \\
&= 0.78\cdot 0.47+0.63\cdot 0.53 \\
& =0.7005 \end{align*}$$
