The mean of the number of tails in three tosses of a coin is :

The correct answer is Option (1) → \( \displaystyle\frac{3}{2} \)

Let X be the number of tails in three tosses. X can be 0, 1, 2 or 3:

    \( \displaystyle P(X=0)=\frac{1}{8} \)

    \( \displaystyle P(X=1)=\frac{3}{8} \)

    \( \displaystyle P(X=2)=\frac{3}{8} \)

    \( \displaystyle P(X=3)=\frac{1}{8} \)

    \( \displaystyle E(X)=0\cdot\frac{1}{8}+1\cdot\frac{3}{8}+2\cdot\frac{3}{8}+3\cdot\frac{1}{8} \)

    \( \displaystyle =\frac{0+3+6+3}{8} \)

    \( \displaystyle =\frac{12}{8} \)

    \( \displaystyle =\frac{3}{2} \)

Shortcut: X is binomial with n = 3 and p = \( \frac{1}{2} \), so its mean is \( np=3\times\frac{1}{2}=\frac{3}{2} \).