If a coin is tossed n times,then the probabil | vedclass

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(A) The total number of possible outcomes when a coin is tossed $n$ times is $2^n$.The number of ways to get heads an odd number of times is given by

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$\frac{1}{2}$

Vedclass · Answer

(A) The total number of possible outcomes when a coin is tossed $n$ times is $2^n$.The number of ways to get heads an odd number of times is given by the sum of binomial coefficients: $\binom{n}{1} + \binom{n}{3} + \binom{n}{5} + \dots$It is a known property of binomial coefficients that the sum of odd-indexed terms is equal to the sum of even-indexed terms,which is $2^{n-1}$.Therefore,the number of favorable outcomes is $2^{n-1}$.The required probability is $\frac{	ext{Favorable outcomes}}{	ext{Total outcomes}} = \frac{2^{n-1}}{2^n} = \frac{1}{2}$.

If a coin is tossed $n$ times,then the probability that the head comes up an odd number of times is:

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