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    Confused_111's Avatar
    Confused_111 Posts: 19, Reputation: 1
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    #1

    Oct 22, 2007, 03:19 AM
    Probablity again.
    Here is another question I find difficult to comprehend for me...

    If Pr(A)=0.7, Pr (A Intersection B)=0.32 and the Pr(A` Intersection B`)=0.10, then the Pr (B)=

    I know the formula Pr(A Union B)=Pr(A)+Pr(B)-Pr(A Intersection B) but don't know what the dashes mean and how to work out Pr(B)
    terryg752's Avatar
    terryg752 Posts: 197, Reputation: 4
    Junior Member
    		  
    #2

    Oct 22, 2007, 06:09 PM
    In Set theory:

    Complement of Union = Intersection of complements (Demorgan's Laws)

    (A U B)` = (A` intersection B`)

    Hence Pr (A U B)` = .10

    Hence Pr (A U B) = 1 - .10 = .9
    Hence

    Pr (A) + Pr (B) - Pr (A intersection B) = .9

    Hence

    .7 + Pr (B) - .32 = .9

    Pr (B) = .9 - .7 + .32 = .52
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