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Conditional Probability

In Probability,

In the real world, probabilities are not straightforward, like P→QP \rightarrow Q. Therefore we translate into P(B∣A)≈1P(B|A) \approx 1. If AA happens, then B is most likely to happen. This defines as

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

This means

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

P(B∣A)P(B|A) is the likelihood and P(A)P(A) is the prior.