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Math Help - Probability

  1. #1
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    Probability

    If C and D are events such that Pr(C) = 0.6 , Pr(D) = 0.5 and C and D are independent, find
    a Pr(C|D)
    b Pr(C U D)
    I am unsure how to start, as I don't know what the symbols represent and what is needed?
    Any help would be greatly appreciated!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by scubasteve94 View Post
    If C and D are events such that Pr(C) = 0.6 , Pr(D) = 0.5 and C and D are independent, find
    a Pr(C|D)
    b Pr(C U D)
    I am unsure how to start, as I don't know what the symbols represent and what is needed?
    Any help would be greatly appreciated!
    Pr(X) denotes the probability of X

    Pr(X|Y) denotes the probability that X occurs given that Y occurs

    Pr(X U Y) denotes the probability of the union of events X and Y, that is the probability that one or other or both occur.

    If C and D are independednt Pr(C and D)=Pr(C)Pr(D) - this is the definition of independednce.

    Also: Pr(C and D)=Pr(C|D)Pr(D).

    That should be sufficient to do part (a)

    For part (b) you need:

    Pr(C U D)=Pr(C)+Pr(D)-Pr(C and D)

    CB
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  3. #3
    MHF Contributor matheagle's Avatar
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    equivalent definitions to independence are

    P(C|D)=P(C)
    P(D|C)=P(D)
    and
    P(CD)=P(C)P(D)

    Any of these implies the other two
    and of course if one holds, all three hold
    and if one fails the other two fail

    The first two are the natural definition of independence
    The chance of C happening is the same no matter if D occurs or not.
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