A coin is tossed n times. If the probability | vedclass

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(B) The probability of getting $k$ heads in $n$ tosses of a fair coin is given by the binomial distribution formula: $P(X = k) = \binom{n}{k} (\frac{1

Vedclass · Accepted Answer

$14$

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(B) The probability of getting $k$ heads in $n$ tosses of a fair coin is given by the binomial distribution formula: $P(X = k) = \binom{n}{k} (\frac{1}{2})^n$.Given that $P(X = 6) = P(X = 8)$,we have:$\binom{n}{6} (\frac{1}{2})^n = \binom{n}{8} (\frac{1}{2})^n$.This simplifies to $\binom{n}{6} = \binom{n}{8}$.Using the property $\binom{n}{r} = \binom{n}{n-r}$,we know that if $\binom{n}{a} = \binom{n}{b}$,then either $a = b$ or $a + b = n$.Since $6 
eq 8$,we must have $6 + 8 = n$.Therefore,$n = 14$.

$A$ coin is tossed $n$ times. If the probability of getting $6$ heads is equal to the probability of getting $8$ heads,then find the value of $n$.

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