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

1. mutually exclusive?
2. simple?
3. compound?

Answer 1

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