The following questions are separate questions. (a) Let X and Y be two events such that...

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The following questions are separate questions. (a) Let X and Y be two events such that P(X) = 0.4 and P(Y) = 0.9. Show that P(X nY) 2 0.3. (b) Four dice are tossed. If all 4 of them indicate different numbers, what is the probability that one of them is a 3? (c) Let E and F be two events with P(E) = 0.3. P(F) = 0.8, P(ENF) = 0.2. Compute probabilities: (1) P(E|F) (ii) P(E|F") (Here E' denotes the complement of E) The following questions are separate questions. (a) Let X and Y be two events such that P(X) = 0.4 and P(Y) = 0.9. Show that P(X nY) 2 0.3. (b) Four dice are tossed. If all 4 of them indicate different numbers, what is the probability that one of them is a 3? (c) Let E and F be two events with P(E) = 0.3. P(F) = 0.8, P(ENF) = 0.2. Compute probabilities: (1) P(E|F) (ii) P(E|F") (Here E' denotes the complement of E)