Three coins are tossed once. Let A denote ...

NCERT Class XI Mathematics - Probability - Solutions

Question : 20 of 54

Marks: +1, -0

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?

Solution:

An experiment consists of tossing three coins.

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

∴ A : Three heads show = {HHH}

B : Two heads and one tail show = {HHT, HTH, THH}

C : Three tail show = {TTT}

D : A head show on the first coin = {HHH, HHT, HTH, HTT}

(i) Since A ∩ B = ϕ, A ∩ C = ϕ, B ∩ C = ϕ, C ∩ D = ϕ.

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

(ii) A and C are simple events.

(iii) B and D are compound events.

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