Question

Consider a situation in which P(X) = and P(Y) = . If P(X and Y) is = , which best describes the events?

They are independent because P(X) · P(Y) = P(X and Y).
They are independent because P(X) + P(Y) = P(X and Y).
They are dependent because P(X) · P(Y) = P(X and Y).
They are dependent because P(X) + P(Y) = P(X and Y).

Answer 1

They are independent because independence means P(X and Y) = P(X)·P(Y). The equality with a sum is not the criterion (P(X)+P(Y)=P(X and Y) is not generally true).