Statistics

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Events A, B, and C are defines on sample space S. Their corresponding sets of sample points do not intersect and their union is S. Further, event B is twice as likely to occur as event A, and event C is twice as likely to occur as event B. Determine the probability of each of these three events.

  • Statistics -

    Given:
    S=A∪B∪C=sample space
    ∅=A∩B
    ∅=B∩C
    ∅=C∩A
    P(A)=2P(B)
    P(B)=2P(C)

    Therefore
    P(S)=1
    P(A)+P(B)+P(C)=1
    2P(B)+2P(C)+P(C)=1
    4P(C)+2P(C)+P(C)=1
    7P(C)=1
    P(C)=1/7
    Can you find the rest?

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