1. [40 pts]. A communication network has two paths controlled by five switches as shown below. In order to communicate, one or more paths must be fully connected between X and Y. The probability that each switch is closed is: Pr(a) = 5/7 Pr(b) = 1/2 Pr(c) = 3/5 Pr(d) = 1/2 Pr(e) = 2/5 Pr(f) = = 4/7 a b d e (a) (b) (c) (d) If switch "P" becomes stuck in the open position, new Pr(f) = 010, what is the probability that an electrical signal transmitted from node X will be received at node Y? If switch "a" becomes stuck in the open position, new Pr(a) = %10, what is the probability that an electrical signal transmitted from node X will be received at node Y? For all switches working based on their probabilities, what is the probability that an electrical signal transmitted from node X will be received at node Y? If you know that a signal is being transmitted from node X to node Y, what is the conditional probability that the path2 = n (dUe) switch path is transmitting (f closed along with either d or e or both closed)? Hint: Bayes Theorem should be applied.