Question

An ordinary die is thrown. Find the probability that the number obtained is a multiple of 2 and the probability that it is less than 4

Answer 1

Task. An ordinary die is thrown. Find the probability that the number obtained is a multiple of 2 and the probability that it is less than 4.

Solution. Let $X$ be the random variable equal to the number obtained on the die. Then for every $i=1,\ldots,6$

$P(X=i)=\frac{1}{6}.$

Let $A$ be the event that the number of the die is a multiple of 2. This may happens only when $X=2,4,6$, hence

$P(A)=P(X=2)+P(X=4)+P(X=6)=\frac{3}{6}=0.5.$

Let $B$ be the event that the number of the die is less than 4. This may happens only when $X=1,2,3$, hence

$P(B)=P(X=1)+P(X=2)+P(X=3)=\frac{3}{6}=0.5.$