Three coins are tossed once. Let A denote the event ‘three heads sho

1.	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 can’. Which events are (i) mutually exclusive? (ii) simple ? (iii) compound?
Answer» We have, sample space = S = {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT) Then A = {HHH} B = {HHT, HTH, THH} C = {T,T,T} D = {HHH, HTH, HHT, HTT} (i) Clearly A ∩ B = ϕ, A ∩ C = ϕ, C ∩ D = ϕ ⇒ A and B ,A and C ; C and D are mutually exclusive. (ii) A, C are simple events. (iii) B, D are compounds events.

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 can’. Which events are (i) mutually exclusive? (ii) simple ? (iii) compound?

Answer»

We have, sample space

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

Then

A = {HHH}

B = {HHT, HTH, THH}

C = {T,T,T}

D = {HHH, HTH, HHT, HTT}

(i) Clearly A ∩ B = ϕ, A ∩ C = ϕ, C ∩ D = ϕ

⇒ A and B ,A and C ; C and D are mutually exclusive.

(ii) A, C are simple events.

(iii) B, D are compounds events.

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