Question

A box contains different-colored marbles. If P(blue) = , P(green) = , and P(blue and green) = , which statement is true?

The events are independent because P(blue) P(green) = P(blue and green).
The events are independent because P(blue) P(green) P(blue and green).
The events are dependent because P(blue) P(green) = P(blue and green).
The events are dependent because P(blue) P(green) P(blue and green).

Answer 1

Independence holds exactly when P(blue and green) = P(blue)·P(green). So the true statement is:

"The events are independent because P(blue)·P(green) = P(blue and green)."

If instead the product is not equal to the joint probability, the events are dependent.