#### 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

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

\[\text{ Let X denote the number of heads obtained in 10 tosses of a coin } . \]

\[\text{ Then, X follows a binomial distribution with n = 6 } , p = \frac{1}{2} = q\]

\[\text{ The distribution is given by } \]

\[P(X = r) = ^{10}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{10 - r} \]

\[ \therefore P(X = 6) = \frac{^{10}{}{C}_6}{2^{10}}\]

\[ = \frac{105}{2^9}\]

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

Is there an error in this question or solution?

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A Coin is Tossed 10 Times. the Probability of Getting Exactly Six Heads is Concept: Bernoulli Trials and Binomial Distribution.

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