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 \(D\) denotes the event a head shows on the first coin”. Which events are (I) mutually exclusive? (ii) simple? (iii) Compound?

Answer 1

Sample Space:

When three coins are tossed once,

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

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Given Events:

A = Three heads show = { HHH }
B = Two heads and one tail show = { HHT, HTH, THH }
C = Three tails show = { TTT }
D = A head shows on the first coin = { HHH, HHT, HTH, HTT }

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(i) Mutually exclusive events

Events are mutually exclusive if they have no common outcomes.

A ∩ B = ∅, A ∩ C = ∅, B ∩ C = ∅

Hence, the mutually exclusive events are:
A and B, A and C, B and C

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(ii) Simple events

A simple event contains only one outcome.

Event A = { HHH }
Event C = { TTT }

Hence, the simple events are:
A and C

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(iii) Compound events

A compound event contains more than one outcome.

Event B = { HHT, HTH, THH }
Event D = { HHH, HHT, HTH, HTT }

Hence, the compound events are:
B and D

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Final Summary:

Mutually exclusive events: A & B, A & C, B & C
Simple events: A, C
Compound events: B, D