Solutions - 5040-01

(1) Define events:

Let $W$ = she watches the computer, $S$ = computer is stolen.

Given: $P[S|W]=0.1$, $P[S|W^c]=0.7$, $P[W]=0.9$.

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(2) Apply Bayes’ Theorem:

$$\begin{array}{c}P[W|S]=\frac{P[S|W]P[W]}{P[S]}\\ \\ \gg \gg \frac{P[S|W]P[W]}{P[S|W]P[W]+P[S|W^c]P[W^c]}\\ \\ \gg \gg \frac{0.1\cdot 0.9}{0.1\cdot 0.9+0.7\cdot 0.1}\gg \gg 0.5625\end{array}$$