Question

Let event A = You roll an even number on the first cube.

Let event B= You roll a 4 on the second cube.
Are the events independent or dependent? Why?
A. Independent, because the outcome of the first roll doesn't affect
the outcome of the second roll.
B. Independent, because they have no outcomes in common.
C. Dependent, because 4 is an even number.
OD. Dependent, because both cubes have six sides.

Answer 1

The events A and B are independent, because the outcome of rolling an even number on the first cube doesn't affect the outcome of rolling a 4 on the second cube. The events don't have any outcomes in common, and the fact that both cubes have six sides doesn't necessarily make them dependent. The probability of rolling an even number on the first cube is 3/6, or 1/2, and the probability of rolling a 4 on the second cube is 1/6, so the probability of rolling an even number on the first cube and then rolling a 4 on the second cube is (1/2) x (1/6) = 1/12. This probability is the same whether the rolls are done in sequence or simultaneously, which is another way of showing that the events are independent.