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Given P(A B) = 0. Find P(A|B).

Mathematics

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Here's a step-by-step solution to question 8:

Part i)

a) Given P(A∩B)=0P(A \cap B) = 0. Find P(A∣B)P(A|B).

  1. Recall the formula for conditional probability.

    P(A∣B)=P(A∩B)P(B)P(A|B) = \frac{P(A \cap B)}{P(B)}

  2. Substitute the given value P(A∩B)=0P(A \cap B) = 0.

    P(A∣B)=0P(B)P(A|B) = \frac{0}{P(B)}

  3. Simplify the expression.

    Assuming P(B)>0P(B) > 0,

    P(A∣B)=0P(A|B) = 0

    a) 0\boxed{0}

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