Is joint probability the same as intersection?

Let A and B be the two events, joint probability is the probability of event B occurring at the same time that event A occurs. This can be written as P(A, B) or P(A ⋂ B). Here, the symbol “⋂” denotes the intersection of event A and B, i.e. the common elements of both the sets A and B. Thus, the joint probability is also called the intersection of two or more events. 

 

In terms of random variables X and Y, the joint probability can be determined using the following representation.

f(x,y) = P(X = x, Y = y)

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