# A Coin is Tossed 10 Times. the Probability of Getting Exactly Six Heads is - Mathematics

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