Question

Find the probability distribution of the number of heads, when three coins are tossed.

Answer 1

Let X denote the number of heads in three tosses of a coin. Then, X can take the values 0, 1, 2 and 3.
Now,
$$\begin{gathered} P\left(X=0\right)=P\left(TTT\right)=\frac{1}{8},P\left(X=1\right)=P\left(HTT\mathrm{or}TTH\mathrm{or}THT\right)=\frac{3}{8} \\ P\left(X=2\right)=P\left(HTH\mathrm{or}THH\mathrm{or}HHT\right)=\frac{3}{8},P\left(X=3\right)=P\left(HHH\right)=\frac{1}{8} \end{gathered}$$

Thus, the probability distribution of X is given by

X	P (X)
0	$\frac{1}{8}$
1	$\frac{3}{8}$
2	$\frac{3}{8}$
3	$\frac{1}{8}$