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Get Answers to all your Questions
5. Three coins are tossed. Describe
(ii) Three events which are mutually exclusive and exhaustive.
Answers (1)
Sample space when three coins are tossed = [Sample space when a coin is tossed thrice!]
S = {HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}
Let ,
A = Getting no tails = {HHH}
B = Getting exactly one tail = {HHT, HTH, THH}
C = Getting at least two tails = {HTT, THT, TTH}
Clearly, A B =
; B
C =
; C
A =
Since (A and B), (B and C) and (A and C) are mutually exclusive
Therefore A, B and C are mutually exclusive.
Also,
A B
C = S
Hence A, B and C are exhaustive events.
Hence, A, B and C are three events which are mutually exclusive and exhaustive.
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