Question

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

• A. $\frac{512}{513}$
• B. $\frac{105}{512}$
• C. $\frac{100}{153}$
• D. ${}^{10}{C}_8$

Answer 1

The correct option is B $\frac{105}{512}$

If a coin a is tossed then the probability of getting head and getting tail is $\frac{1}{2}$.

Now, if the coin is tossed $10$ times then the probability of getting exactly $6$ heads is,

${}^{10}{C}_6\times {\left(\frac{1}{2}\right)}^6\times {\left(\frac{1}{2}\right)}^4$

$=\frac{210}{2^{10}}$

$=\frac{105}{2^9}$

$=\frac{105}{512}$.