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Get Answers to all your Questions
4. Three coins are tossed once. Let A denote the event ‘three heads show”, B denote the event “two heads and one tail show”, C denote the event” three tails show and D denote the event ‘a head shows on the first coin”. Which events are
(i) mutually exclusive?
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}
Now,
A = Event that three heads show up = {HHH}
B = Event that two heads and one tail show up = {HHT, HTH, THH}
C = Event that three tails show up = {TTT}
D = Event that a head shows on the first coin = {HHH, HHT, HTH, HTT}
(i). For two elements X and Y to be mutually exclusive, X Y =
A B = {HHH}
{HHT, HTH, THH} =
; Hence A and B are mutually exclusive.
B C = {HHT, HTH, THH}
{TTT} =
; Hence B and C are mutually exclusive.
C D = {TTT}
{HHH, HHT, HTH, HTT} =
; Hence C and D are mutually exclusive.
D A = {HHH, HHT, HTH, HTT}
{HHH} = {HHH} ; Hence D and A are not mutually exclusive.
A C = {HHH}
{TTT} =
; Hence A and C are mutually exclusive.
B D = {HHT, HTH, THH}
{HHH, HHT, HTH, HTT} = {HHT, HTH} ; Hence B and D are not mutually exclusive.
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