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 :

2

The correct answer is Option (3) → 2

1 appears on 3 faces

1 appears on 2 faces

1 appears on 1 face

Mean, $E(X)=∑(x_i×P(x_i))$

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

$E(X)=\left(1×\frac{1}{2}\right)+\left(2×\frac{1}{3}\right)+\left(5×\frac{1}{6}\right)$

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

$=\frac{12}{6}=2$