you roll a fair number cube twice. what is the probability of rolling two 3's if the first roll is 5

is the answer 2/25

To find the probability of two events occurring, we multiply the probabilities of each event.

We know that the cube is fair, which means it has 6 equally likely outcomes: 1, 2, 3, 4, 5, and 6.

If the first roll is fixed at 5, there is only 1 outcome that satisfies this condition. So the probability of getting a 5 on the first roll is 1/6.

For the second roll, we are interested in rolling a 3. Since the number cube is fair, there is again only 1 outcome that satisfies this condition (rolling a 3), and a total of 6 possible outcomes (1, 2, 3, 4, 5, and 6). Therefore, the probability of rolling a 3 on the second roll is 1/6.

To find the probability of both events occurring, we multiply the probabilities:

(1/6) * (1/6) = 1/36.

Therefore, the probability of rolling two 3's with the first roll being a 5 is 1/36.