A binary sequence is an array of 0's and 1's. | vedclass

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(A) Let $S$ be the set of all $n$-digit binary sequences. The total number of such sequences is $2^n$.Let $E$ be the number of sequences with an even

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$2^{n-1}$

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(A) Let $S$ be the set of all $n$-digit binary sequences. The total number of such sequences is $2^n$.Let $E$ be the number of sequences with an even number of $0$'s and $O$ be the number of sequences with an odd number of $0$'s.We know that the sum of binomial coefficients ${}^n C_0 + {}^n C_2 + {}^n C_4 + \dots = 2^{n-1}$.This sum represents the number of ways to choose an even number of positions for $0$'s in an $n$-digit sequence.Therefore,the number of such sequences is $2^{n-1}$.

$A$ binary sequence is an array of $0$'s and $1$'s. The number of $n$-digit binary sequences which contain an even number of $0$'s is

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