Question

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 ? (ii) simple ? (iii) compound ?​

Answer 1

Answer:

When three coins are tossed the sample space is given by,

S={HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}

A={HHH}

B={HHT,HTH,THH}

C={TTT}

D={HHH,HHT,HTH,HTT}

A∩B=ϕ

A∩C=ϕ

A∩D={HHH}



=ϕ

B∩C=ϕ

B∩D={HHT,HTH}



=ϕ

C∩D=ϕ

(i) Event A and B; event A and C; event B and C; and event C and D are all mutually exclusive.

(ii) If an event has only one sample point of a sample space, it is called a simple event.

Thus A and C are simple 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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Hope it was helpful (◕ᴗ◕✿)