Question

You roll two dice. What are the probability that the sum of the numbers on the dice is odd and both dice show the number $5$?

Answer 1

Find the required probability.

Recall that the probability of an impossible event is $0$. If both the dice show the number $5$, then the sum of the numbers must be $5+5=10$, which is even. So, the event that the sum of the numbers on the dice is odd cannot occur together with the event that both dice show the number $5$. Thus, the event that the sum of the numbers on the dice is odd and that both dice show the number $5$, is an impossible event with probability $0$.

Hence, the probability that the sum of the numbers on the dice is odd and that both dice show the number $\mathbf{5}$ is $\mathbf{0}$.