Three intermittent switches A; B; C are in a box. Switches A; B and C work 75%, 50% and 25% of the time, respectively. Suppose switches are selected with equal probability from the box.

(a) Find the probability that the selected switch works

(b) Find the probability that the selected switch is not switch C; given that the selected switch works.

a) probability of selecting working switch = (probability of A getting selected) x (working probability of A) + (probability of B getting selected) x (working probability of B) + (probability of C getting selected) x (working probability of C) = 0.75/3+0.5/3+.25/3=0.5

b) its conditional probability p (A|B) = p (AnB) / p (B) = (0.75/3+0.5/3) / (0.75/3+0.5/3+.25/3) = 5/6=0.833