Question

A coin is tossed 10 times. The probability of getting exactly six heads is

Options

• \[\frac{512}{513}\]

   

• \[\frac{105}{512}\]

   

• \[\frac{100}{153}\]

   

• \[^{10}{}{C}_6\]

   

Answer 1

\[\frac{105}{512}\]

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