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Three fair coins are tossed once. Define events: X = all three heads (HHH), Y = exactly two heads and one tail, Z = all three tails (TTT), W = head on the first coin. Which pairs among (X, Y), (X, Z), and (Y, Z) are mutually exclusive?

1. X, Y only
2. X, Z only
3. Y, Z only
4. All of these

Correct answer: All of these

Solution

X = {HHH}, Y = {HHT, HTH, THH}, Z = {TTT} are pairwise disjoint sets, so each pair (X,Y), (X,Z), and (Y,Z) is mutually exclusive.

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