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Question
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
- mutually exclusive?
- simple?
- compound?
Solution
When three coins are tossed then the sample space
S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
A: Three heads showing = {HHH}
B: Two heads and one tails appearing
= {HHT, HTH, THH}
C: Three tails appearing = {TTT}
D: Heads appear on the first coin
= {HHH, HHT, HTH, HTT}
i. A ∩ B = {HHH} ∩ {HHT, HTH, THH}
= ϕ
A ∩ C = {HHH} ∩ {TIT} = ϕ
A ∩ D = {HHH} {HHH, HHT, HTH, HTT}
= {HHH} ≠ ϕ
B ∩ C = {HHT, HTH, THH} ∩ {TTT}
= ϕ
B ∩ D = {HHT, HTH, THH) ∩ {HHH, HHT, HTH, HTT}
= (HHT, HTH} ≠ ϕ
C ∩ D = {TTT} {HHH, HHT, HTH, HTT}
ϕ
A ∩ B ∩ C = {HHH} ∩ {HHT, HTH, THH} ∩ {TTT)
= ϕ
So mutually exclusive events
A and B, A and C, B and C, C and D, A, B and C
ii. Simple events: A and C
iii. Compound events: B and D
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