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What is the definition of conditional probability?
Is the probability that a and b happen at the same time. Like throwing dice,

A: The number of points is less than or equal to 4 points.

B: throw a red idea.

We know that P(A)=4/6=2/3, (because only 5 and 6 are greater than 4 points).

P(B)=2/6= 1/3, (because 1 and 4 in the dice are red. )

So P(AB)=P (the casting point is less than or equal to 4 points and red, and 1 is consistent with 4 points) = 1/3.

For conditional probability, it is generally believed that one event is known, so what is the probability of another event? For example, if you throw a dice and you see it is red, what is the probability that A will happen now, that is, the number of points will not exceed 4? Intuitively, it is 1, because once it is red, it cannot be greater than 4. So, mathematically,

P (a | b) (probability of a when b occurs)

=P(AB)/P(B)

= 1.

This is consistent with intuitive feeling.