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 $2$

Given a die having written $1$ on three faces, $2$ on two faces and $5$ on one face.
Let $X$ be the random variable representing a number on given die.
Then $X$ can take any value of $1,2$ or $5.$
The total numbers is six.
Now
$P(X=1)=3/6=1/2$
$P(X=2)=1/3$
$P(X=5)=1/6$
Hence, the required probability distribution is,
$\begin{array}{cccc}\text{X}& \text{1}& \text{2}& \text{5}\\ \text{P(X)}& \text{1/2}& \text{1/3}& \text{1/6}\end{array}$
Therefore, Expectation of $X$ is
$E\left(X\right)=\sum _{i=1}^n{x}_i{p}_i$
Now by substituting the values we get
$=1\times \frac{1}{2}+2\times \frac{1}{3}+5\times \frac{1}{6}=\frac{1}{2}+\frac{2}{3}+\frac{5}{6}=\frac{3+4+5}{6}=\frac{12}{6}\Rightarrow E\left(X\right)=2$