Question

Three coins are tossed once. Describe the following events associated with this random experiment: A = Getting three heads B = Getting two heads and one tail C = Getting three tails D = Getting a head on the first coin. (i) Which pairs of events are mutually exclusive? (ii) Which events are elementary events? (iii) Which events are compound events?

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Solution

When three coins are tossed, the sample space is given by S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Accordingly, we have: A = {HHH} B = {HHT, HTH, THH} C = {TTT} D = {HHH, HHT, HTH, HTT} Now, we observe that A ∩ B = Φ; A ∩ C = Φ; A ∩ D = {HHH} ≠ Φ; B ∩ C = Φ; B ∩ D = {HHT, {HTH} ≠ Φ and C ∩ D = Φ (i) Events A and B; events A and C; events B and C and events C and D are all mutually exclusive. (ii) If an event has only one sample point of a sample space, it is called an elementary event. Thus, A and C are elementary events. (iii) If an event has more than one sample point of a sample space, it is called a compound event. Thus, B and D are compound events.

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