Points$]$

DEVORESTAT$92\mathrm{.}5\mathrm{.}084.$

Consider purchasing a system of audio components consisting of a receiver, a pair of speakers, and a CD player. Let $A_1$ be the event that the receiver functions properly throughout the warranty period, $A_2$ be the event that the speakers function properly throughout the warranty period, and $A_3$ be the event that the CD player functions properly throughout the warranty period. Suppose that these events are $($mutually$)$ independent with $P(A_1)=0\mathrm{.}96,P(A_2)=0\mathrm{.}92,$ and $P(A_3)=0\mathrm{.}90.($Round your answers to four decimal places.$)$

$($a$)$ What is the probability that all three components function properly throughout the warranty period?

$($b$)$ What is the probability that at least one component needs service during the warranty period?

$($c$)$ What is the probability that all three components need service during the warranty period?

$($d$)$ What is the probability that only the receiver needs service during the warranty period?

$($e$)$ What is the probability that exactly one of the three components needs service during the warranty period?

Need Help?