Question

Hugo picks a card at random (2 green, 1 magenta, 3 purple), puts it back, and then picks another card at random.

Are these two events dependent or independent?

Answer 1

Independent. Because Hugo replaces the card, the deck composition is the same for the second draw, so the outcome of the first draw does not affect the probabilities for the second.

For example, P(green first) = 2/6 = 1/3 and P(magenta second) = 1/6, and P(green then magenta) = (2/6)(1/6) = 1/18 = P(green)P(magenta), showing independence.