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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