Question

The mean of the numbers obtained on throwing a die having written 1 on three faces, $2$ on two faces and $5$ on one face is:

• A. $1$
• B. $2$
• C. $5$
• D. $\frac{8}{3}$

Answer 1

The correct option is B $2$

Let $X$ be the random variable representing a number on the die.
The total number of observations is six.
$\therefore P(X=1)=\frac{3}{6}=\frac{1}{2}$
$P(X=2)=\frac{2}{6}=\frac{1}{3}$
$P(X=5)=\frac{1}{6}$
Therefore, the probability distribution is as follows.
Mean $E\left(X\right)=\sum p_i{x}_i$
$=\frac{1}{2}\times 1+\frac{1}{3}\times 2+\frac{1}{6}\times 5$
$=\frac{1}{2}+\frac{2}{3}+\frac{5}{6}$
$=\frac{3+4+5}{6}$
$=\frac{12}{6}$
$=2$