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Question

# Three coins are tossed. Describe (i) two events A and B which are mutually exclusive. (ii) three events A, B and C which are mutually exclusive and exhaustive. (iii) two events A and B which am not mutually exclusive. (iv) two events A and B which are mutually exclusive but not exhaustive.

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Solution

## If three coins are tossed, then possible number of out comes =23=8 Sample space S = {HHH, HHT, writ H1T, TI IH,THT, TTH, TTT} (i) Let A he the event. 'three heads show' ⇒ A = {HHH} and B be the event 'three tails show'. ⇒ B= (TTT) ⇒ A∩B=ϕ Hence. A and B are mutually exclusive events. (ii) Let A be the event 'atleast one head' a ⇒ A= {HHH, HHT, HTH, HTT, THH,THT, TTH} and B be the event getting three tails. ⇒ B = {TTT} ⇒A∩B=ϕandA∪B=S (Two events are exhaustive if A∩B=S) Hence, A and B are naturally exclusive and exhaustive. (iii) Let A be the event 'three heads show' and B be the event 'atleast two heads show' ⇒ A = {HHH} and B = {HHT, HTH, THH, HHH} ⇒A∩B=HHH≠ϕ Hence, A and B are not mutually exclusive. (iv) Same as in (iii) A and B are not mutually exclusive. Also, A∪B≠S.

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