Consider sending packets through a switch with two packet$-$switched channels

$($Channel A and Channel B$).$ Suppose that $40\%$ of the packets are routed via

Channel A$,$ and suppose:

$1\%$ of the packets are lost on Channel A; and

$0\mathrm{.}5\%$ of the packets are lost on Channel B$.$

a$.$ If one packet is sent, find the probability that it is lost.

b$.$ If a packet is lost, what is the probability that it was sent via Channel A$?$

c$.$ If three packets are sent, what is the probability that all three packets are lost?