? asked in Science & MathematicsMathematics · 9 years ago

Statistics question: What is P(A'|B)?

I am doing stats and my question is... What is P(A'|B)?

Given: P(A) = 0.30, P(B') = 0.50, P(B) = 0.50, P(A') = 0.70, P(A intersect B') = 0.10, P(A intersect B) = 0.70....

I would really appreciate the help.... thanks!

Update:

CORRECTION: P(A in union with B) = 0.70 not P(A intersect B) = 0.70

2 Answers

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  • 9 years ago
    Favorite Answer

    P(A' | B) = P(A' and B) / P(B)

    P(A|B) = P(A and B) / P(B)

    You can verify using a Venn diagram that

    P(A' and B) + P(A and B) = P(B)

    and so

    P(A'| B) + P(A|B) = 1

    So Let's find P(A|B).

    Step 1: Find P(A intersect B)

    P(A U B) = P(A) + P(B) - P(A intersect B)

    0.70 = 0.30 + 0.50 - P(A intersect B)

    So

    P(A intersect B) = 0.10

    Step 2: Find P(A|B)

    P(A|B) = P(A intersect B) / P(B)

    = 0.10 / 0.50

    = 0.20

    So P(A|B) = 0.20.

    Step 3: Find P(A' | B)

    Since

    P(A' | B) + P(A | B) = 1

    Then

    P(A' | B) = 1 - P(A | B)

    = 1 - 0.20

    = 0.80

    So P(A' | B) = 0.80.

    Solution: P(A' | B) = 0.80.

    Source(s): ____________ P(A' | B) = P(A' and B) / P(B) P(A | B) = P(A and B) / P(B) P(A' | B) + P(A | B) = [P(A' and B) + P(A and B)] / P(B) Since P(A' and B) + P(A and B) = P(B), then P(A' | B) + P(A | B) = P(B) / P(B) = 1
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  • Anonymous
    9 years ago

    P(A'| B) + P(A|B) = 1

    Now, P(A|B)=P(A intersect B) / P(B)

    Need to find P(A intersect B).

    P(A intersect B) =P(B)+P(A)-P(A union B) [As, P(A union B)=P(B)+P(A)-P(A intersect B)]

    =0.50+0.30-0.70

    =0.10

    So, P(A|B)=0.10/0.50

    =0.20

    Therefore, P(A'| B) = 1- P(A|B)

    =1-0.20

    =0.80 (Ans.)

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