What is 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?

2

The correct answer is Option (3) → 2

Given on three faces of a die 1 is written, on two faces 2 is written and on one face 5 is written.

The die is thrown once. The sample space of the random experiment = {1, 1, 1, 2, 2, 5}. It has six equally likely outcomes.

$∴P(1)=\frac{3}{6}=\frac{1}{2},P(2)=\frac{2}{6}=\frac{1}{3}$ and $P(5)=\frac{1}{6}$.

∴ Probability distribution of the numbers written on face of a die:

Mean $∑p_ix_i=\frac{1}{2}×1+\frac{1}{3}×2+\frac{1}{6}×5=\frac{1}{2}+\frac{2}{3}+\frac{5}{6}$

$=\frac{3+4+5}{6}=\frac{12}{6}=2$