The cube is rolled twice. What is the probability that an even number will be rolled both times?

Answer 1

So you want to use "and" language for this term. You have two conditions. You roll an even number the first time, AND you roll an even number the second time. There are three even numbers in one die, assuming by "cube", you mean a standard die. 3/6 is equal to 1/2. The equation goes like this:

1/2 x 1/2 = 1/4

You multiply because the word "and" is part of the condition.

Answer 2

You deserve a comprehensive explanaton.

For events that are equally likely:

Probability = (number of successes) / (total number of possible outcomes)

A cube has six sides. If they are numbered 1, 2, 3, 4, 5, 6 (six possibilities) and the even ones (2, 4, 6) are successes, then the probability of rolling an even number on the first roll is 3/6 = 1/2.

Now, rolling an even number on the second roll is only important to us (note "AND") if an even number has already been rolled. So, this probability is 1/2 of 1/2 = 1/4

P = 1/4 [note that 0 ≤ P ≤ 1]

Answer 3

(1/2)², assuming you mean a standard die.