Question

An unbiased coin is tossed $n$ times. The probability that head will present itself, odd number of times is

• A. $\frac{1}{4}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $\frac{1}{5}$

Answer 1

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

Total cases when coin is tossed $n$ times $=2^n$
Head will present itself, odd number of times is in half the cases of total $=\frac{2^n}{2}=2^{n-1}$
Probability that head will present itself, odd number of times is$=\frac{2^{n-1}}{2^n}=\frac{1}{2}$