Question

A bag contains a variety of different-colored marbles. If P(red) = , P(green) = , and P(red and green) = , which statement is true?

The events are independent because P(red) • P(green) = P(red and green).
The events are independent because P(red) + P(green) = P(red and green).
The events are dependent because P(red) • P(green) ≠ P(red and green).
The events are dependent because P(red) + P(green) ≠ P(red and green).

Answer 1

Independence is tested by the product rule: events A and B are independent exactly when
P(A and B) = P(A) × P(B).

So:
- If P(red) · P(green) = P(red and green), the first statement is true.
- If P(red) · P(green) ≠ P(red and green), the third statement is true.

The statements involving a sum (the second and fourth) are not the correct test for independence.