Engineering
Mathematics
Conditional Probability
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
(i) mutually exclusive ?
(ii) simple ?
(iii) compound ?

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Solution
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When three coins are tossed the sample space is given by,

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

A = {HHH}

B = {HHT, HTH, THH}

C = {TTT}

D = {HHH, HHT, HTH, HTT}

A∩B = ϕ

A∩C = ϕ

A∩D = {HHH} ≠ ϕ

B∩C = ϕ

B∩D = {HHT, HTH} ≠ ϕ
C∩D = ϕ
(i) Event A and B; event A and C; event B and C; and event C and D are all mutually exclusive.
(ii) If an event has only one sample point of a sample space, it is called a simple event.
Thus A and C are simple events.
(iii) If an event has more than one sample point of a sample space it is called a compound event. Thus B and D are compound events

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