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,

\[P\left( X = 0 \right) = P\left(\text{ TTT }\right) = \frac{1}{8}, P\left( X = 1 \right) = P\left(\text{HTT or TTH or THT }\right) = \frac{3}{8}\]
\[P\left( X = 2 \right) = P\left(\text{ HTH or THH or HHT }\right) = \frac{3}{8}, P\left( X = 3 \right) = P\left( HHH \right) = \frac{1}{8}\]

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	\[\frac{1}{8}\]