If a fair coin is tossed 10 times,find the pr | vedclass

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(A) The repeated tosses of a coin are Bernoulli trials. Let $X$ denote the number of heads in an experiment of $10$ trials.Clearly,$X$ follows a binom

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$\frac{105}{512}$

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(A) The repeated tosses of a coin are Bernoulli trials. Let $X$ denote the number of heads in an experiment of $10$ trials.Clearly,$X$ follows a binomial distribution with $n=10$ and $p=\frac{1}{2}$.The probability mass function is given by $P(X=x) = ^{n}C_{x} q^{n-x} p^{x}$,where $x = 0, 1, 2, \dots, n$.Here,$n=10$,$p=\frac{1}{2}$,and $q=1-p=\frac{1}{2}$.Therefore,$P(X=x) = ^{10}C_{x} (\frac{1}{2})^{10-x} (\frac{1}{2})^{x} = ^{10}C_{x} (\frac{1}{2})^{10}$.For exactly six heads,we set $x=6$:$P(X=6) = ^{10}C_{6} (\frac{1}{2})^{10} = \frac{10!}{6! 	imes 4!} 	imes \frac{1}{1024}$.$P(X=6) = \frac{10 	imes 9 	imes 8 	imes 7}{4 	imes 3 	imes 2 	imes 1} 	imes \frac{1}{1024} = 210 	imes \frac{1}{1024} = \frac{210}{1024} = \frac{105}{512}$.

If a fair coin is tossed $10$ times,find the probability of exactly six heads.

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