2n unbiased coins are tossed. The probability | vedclass

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Question

(B) When $2n$ unbiased coins are tossed, the total number of outcomes is $2^{2n}$.The probability of getting $r$ heads in $2n$ tosses is given by the

Vedclass · Accepted Answer

$1 - \frac{(2n)!}{(n!)^2} \cdot \frac{1}{2^{2n}}$

Vedclass · Answer

(B) When $2n$ unbiased coins are tossed, the total number of outcomes is $2^{2n}$.The probability of getting $r$ heads in $2n$ tosses is given by the binomial distribution: $P(r) = \frac{1}{2^{2n}} \binom{2n}{r}$.The number of heads is equal to the number of tails when the number of heads is exactly $n$.The probability of getting exactly $n$ heads is $P(n) = \frac{1}{2^{2n}} \binom{2n}{n} = \frac{1}{2^{2n}} \cdot \frac{(2n)!}{(n!)^2}$.The probability that the number of heads is not equal to the number of tails is $1 - P(n)$.Therefore, the required probability is $1 - \frac{(2n)!}{(n!)^2} \cdot \frac{1}{2^{2n}}$.

$2n$ unbiased coins are tossed. The probability that the number of heads is not equal to the number of tails is

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