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Question
A coin is tossed 10 times. The probability of getting exactly six heads is
Options
\[\frac{512}{513}\]
\[\frac{105}{512}\]
\[\frac{100}{153}\]
\[^{10}{}{C}_6\]
Solution
\[\frac{105}{512}\]
\[\text{ Let X denote the number of heads obtained in 10 tosses of a coin } . \]
\[\text{ Then, X follows a binomial distribution with n = 6 } , p = \frac{1}{2} = q\]
\[\text{ The distribution is given by } \]
\[P(X = r) = ^{10}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{10 - r} \]
\[ \therefore P(X = 6) = \frac{^{10}{}{C}_6}{2^{10}}\]
\[ = \frac{105}{2^9}\]
\[ = \frac{105}{512}\]
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