Question

Let event A = You roll an even number on the first cube.Let event B = You roll a 6 on the second cube.Are the events independent or dependent? Why?

Answer 1

The events are independent. By definition, it means that knowledge about one event does not help you predict the second, and this is the case: even if you knew that you rolled an even number on the first cube, would you be more or less confident about rolling a six on the second? No.

An example in which two events about rolling cubes are dependent could be something like:

Event A: You roll the first cube

Event B: The second cube returns a higher number than the first one.

In this case, knowledge on event A does change you view on event B (and vice versa): if you know that you rolled a 6 on the first cube you don't want to bet on event B, while if you know that you rolled a 1 on the first cube, you're certain that event B will happen.

Conversely, if you know that event B has happened, you are more likely to think that the first cube rolled a small number, and vice versa.