Question

Two dice were thrown and it is known that the numbers which come up were different. Find the probability that the sum of the two numbers was$5.$

Answer 1

Finding the probability that the sum of the two numbers was$5$:

A is the event such that the sum of the two numbers that came up is 5 and B is the event that the two dice showed different numbers.

$A=(2,3),(3,2),(1,4),(4,1)$

$n\left(A\right)=4$

$n\left(B\right)=30$ cases

Required probability

$$\begin{gathered} =P\left(\frac{A}{B}\right) \\ =\frac{n(A\cap B)}{n\left(B\right)} \\ =\frac{4}{30} \\ =\frac{2}{15} \end{gathered}$$

Therefore, the required probability will be $\frac{2}{15}$.