Question

Two unbiased dice are thrown simultaneously. What is the probability of getting at most one five in a single throw of the two dice?

Answer 1

When two dices are thrown simultaneously, the total number of cases are formed are $36$.

So, we need to find the cases of getting at most one five in a single throw of the two dices.

Therefore, the cases are $\left(1,5\right),\left(2,5\right),\left(3,5\right),\left(4,5\right),\left(5,1\right),\left(5,2\right),\left(5,3\right),\left(5,4\right),\left(5,6\right),\left(6,5\right)$

So, the favourable outcome are $10$.

Now, we know that

$$\begin{gathered} Probability(atmostone5ina\sin gledice)=\frac{Favourableoutcomes}{Totalnumberofoutcomes} \\ Probability(atmostone5ina\sin gledice)=\frac{10}{36} \\ Probability(atmostone5ina\sin gledice)=\frac{5}{10} \end{gathered}$$

Hence, the probability of getting at most one five in a single throw of the two dices is $\frac{5}{18}$.