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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 show on the first coin", Which events are (i) mutually exclusive ? (ii) simple ? (iii) compound?


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    Solution

    When three coins are tossed then S
    ={HHH,HHT,HTH,THH,TTH,THT,HTT,TTT}
    A: Three heads show ={HHH}
    B : two heads and one tails show ={HHT,HTH,THH}
    C: Three tails show ={TTT}
    D: a head shows on the first coin ={HHH,HHT,HTH,HTT}
    (i) Now AB=ϕ
    Thus A and B are mutually exclusive events.
    BC=ϕ
    Thus B and C are mutually exclusive events.
    AC=ϕ
    Thus A and C are mutually exclusive events.
    AD={HHH}=ϕ
    Thus A and D are not mutually exclusive events.
    CD=
    Thus C and D are mutually exclusive events.
    (ii) A={HHH}, here n = 1
    Thus A is a simple event.
    C={TTT} Here n = 1
    Thus C is a simple event.
    (iii) B={HHT,HTH,THH}, here n = 3 > 1
    Thus B is a compound event.
    D={HHH.HHT,HTH,HTT}
    here n = 4 > 1
    Thus D is a compound event.


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