(a) Consider two events, E and F in the same sample space. If E occurs 1 out of every 5

times, F occurs 70% of the time, and Pr[E F ] = 0.75, determine Pr[E|F ].

(b) Consider two events, E and F in the same sample space. Suppose that F is three times as likely to occur as both E and F occurring simultaneously. Assume also that the probability of E occurring, given that F occurs, is twice the probability that E occurs. Determine Pr[E].