Given, Shop has equal number of bulbs
$\therefore$ $P(Type 1)$ = $P(Type 2)$ = $0.5$
Probability of bulb lasting more than 100 hr given that it’s $Type – 1$ = $P$($>100hr$ | $Type 1$) = $0.7$
Probability of bulb lasting more than 100 hr given that it’s $Type – 2$ = $P$($>100hr$ | $Type 2$) = $0.4$
$\therefore$ Probability that an LED bulb lasts more than 100 hrs.:
$P(> 100 hr)$ = $P$($>100hr$ | $Type 1$) $\times$ $P(Type 1)$ $+$ $P$($>100hr$ | $Type 2$) $\times$ $P(Type 2)$
$P(> 100 hr)$ = $0.7 \times 0.5 + 0.4 \times 0.5 = 0.35 + 0.20$ = $0.55$ [Ans]