Let $$X$$ be the event "comes from factory $$X$$" and $$Y$$ be the event "comes fom factory $$Y$$ " and Let $$H$$ be the event "works over $$5000$$ hours."

Therefore $$P(X)=60 \%=0.60 \Rightarrow P(Y)=1-0.60=0.40$$

Given that, Factory $$X's$$ bulbs work for over $$5000$$ hours in $$99 \%$$ of cases.

$$\therefore P(H|X)=99 \%=0.99$$

Also given, factory Y's bulbs work for over

$$$000$$5000$$ hours in

%$$95\%$$ of cases.

$$\therefore P(H|Y)=95 \%=0.95$$

Then by the Law of Total Probability we have

$$P(H) = P (H | X) P(X) + P (H | Y ) P(Y ) $$

$$= (.99) (.6) + (.95) (.4)$$

$$ = .974$$

Thus $$P(H)=0.974=\dfrac{974}{1000}$$.