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Let X and Y be two random variables.

Case (1) - Discrete Case

If P(X = x) denotes the probability that the random variable X takes the value x, then the joint probability of X and Y is P(X = x and Y = y).

Case (2) - Continuous Case

If P(a < X < b) is the probability of the random variable X taking a value in the real interval (a, b), then the joint probability of X and Y is P(a < X< b and c < Y < d).

Basically joint probability is the probability of two events happening (or not).

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Q: What is joint probability?
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Can a joint probability have a value greater than 1?

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