The mean of numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on one face is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 2
Let X be the number obtained. Each of the six faces is equally likely, so
\( \displaystyle P(X=1) = \frac{3}{6},\quad P(X=2) = \frac{2}{6},\quad P(X=5) = \frac{1}{6} \)
The mean is \(E(X) = \sum x\,P(X=x)\):
\( \displaystyle E(X) = 1\cdot\frac{3}{6} + 2\cdot\frac{2}{6} + 5\cdot\frac{1}{6} \)
\( \displaystyle = \frac{3 + 4 + 5}{6} = \frac{12}{6} = 2 \)