NCERT Class XI Mathematics - Probability - Solutions
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Question : 20
Total: 54
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?
(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.
∴ 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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