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)
H Harsh Kankaria

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 \cap Y = \phi

\cap B = {HHH} \cap {HHT, HTH, THH} = \phi ; Hence A and B are mutually exclusive.

\cap C = {HHT, HTH, THH} \cap {TTT} = \phi ; Hence B and C are mutually exclusive.

\cap D = {TTT} \cap {HHH, HHT, HTH, HTT} = \phi ; Hence C and D are mutually exclusive.

\cap A = {HHH, HHT, HTH, HTT} \cap {HHH} = {HHH} ; Hence D and A are not mutually exclusive.

\cap C = {HHH} \cap {TTT} = \phi ; Hence A and C are mutually exclusive.

\cap D = {HHT, HTH, THH} \cap {HHH, HHT, HTH, HTT} = {HHT, HTH}  ; Hence B and D are not mutually exclusive.

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