1.3 Conditional Probability

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Example 1.3-10

THIS

Example 1.3-11

THIS

Example 1.3-12

THIS

Example 1.3-6

THIS

Extending multiplication rule for conditional probabilities

THIS read the LHS then try to visualize or solve

Example 1.3-7

THIS you should learn that it is convenient to separate the event into two sections - normal and conditional probabilities - to calculate the intersection of them

The conditional probability of a sum of 3 given that a sum of 3 or 5 has occurred

probability that a sum of 3 is rolled before a sum of 5 is rolled can be thought of as

1. P(A|B) ≥ 0 2. P(B|B) = 1 3. if A₁, A₂, ... are mutually exclusive events, then P(A₁ ∪ A₂ ∪ ... A(k)|B) = P(A₁|B) + P(A₂|B) + ... + P(A(k)|B)

the three axioms for the conditional probability

Deduce P(A|B) from N(A) and N(B)

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Definition of the multiplication rule for the conditional probability

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Example 1.3-9 think of this example as an extension of multiplication rule for conditional probabilities

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P(A|B)

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Prove that 1. P(A|B) ≥ 0 2. P(B|B) = 1 hold

WORD


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