Question

If a coin be tossed $n$ times then the probability that the head comes odd times is

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{1}{6}$

Answer 1

The correct option is C $\frac{1}{2}$

Total number of cases $=2^n$
If head comes odd times $(1,3,5,...)$, then favourable number of ways
$={}^n{C}_1{+}^n{C}_3{+}^n{C}_5+...=2^{n-1}$.
Therefore, the required probability
$=\frac{2^{n-1}}{2^n}=\frac{1}{2}$