Question

Two dice are thrown. What is the probability that the sum of dots shown is 4 or 6?

Answer 1

Task. Two dice are thrown. What is the probability that the sum of dots shown is 4 or 6?

Solution. The set $\Omega$ of all results of throwing two dice is the set of all pairs $(i,j)$, where $i,j\in\{1,2,\ldots,6\}$. Therefore the number $|\Omega|$ of elements in $\Omega$ is equal to $6*6=36$.

Let $A$ be the subset of $\Omega$ consisting of pairs $(i,j)$ such that $i+j$ is equal either to 4 or to 6. Then $A$ is the following set

$A=\{(1,3),(2,2),(3,1),(1,5),(2,4),(3,3),(4,2),(5,1)\}$

So it consists of $|A|=8$ elements.

Then the required probability is equal to

$p=\frac{|A|}{|\Omega|}=\frac{8}{36}=\frac{4}{9}\approx 0.44.$

Answer. $\frac{4}{9}\approx 0.44.$