Question

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

• A. $\frac{1}{2}$
• B. $\frac{1}{2^n}$
• C. $\frac{1}{2^{n-1}}$
• D. None of these

Answer 1

The correct option is A

$\frac{1}{2}$

Explanation for the correct option:

Find the probability required probability:

If a coin is tossed $n$ times, then the total sample space, $n\left(S\right)$ $=2^n$

Now, the number of ways that the head comes in odd times $n\left(E\right)$$={}^{n}C_1+{}^{n}C_3+{}^{n}C_5+....$

$=2^{n-1}$

$\therefore$the required probability $\mathit{P}\mathbf{\left(}\mathit{E}\mathbf{\right)}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{n}\mathbf{\left(}\mathbf{E}\mathbf{\right)}}{\mathbf{n}\mathbf{\left(}\mathbf{S}\mathbf{\right)}}$

$=\frac{2^{n-1}}{2^n}$

$=\frac{\mathbf{1}}{\mathbf{2}}$

Hence, Option ‘A’ is Correct.