Question

a fair coin is tossed 5 times. what is the probability that exactly 2 heads are observed

Answer 1

Answer:

It will be answered as 2tails Mark me as brainliest

Answer 2

Given:

A fair coin is tossed 5 times.

Solution:

To find the probability  of getting  exactly 2 heads apply the negative binomial formula,

$\[ = C_{r - 1}^{n + r - 1}{P^r}{\left( {1 - P} \right)^n}\]$

Here, $\[r\]$ is the number of successes and $n$ is the number of failures,

Therefore, put $\[r = 2\]$ and $\[n = 3\]$,

$\[ = C_1^4 \times {\left( {\frac{1}{2}} \right)^2} \times {\left( {\frac{1}{2}} \right)^3}\]$

$\[ = \frac{4}{{{2^5}}}\]$

$\[ = \frac{1}{8}\]$

Hence,  the probability that exactly 2 heads are observed is $\[\frac{1}{8}\]$.