Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).

Assertion (A): Kuhu and Beena are two equally capable badminton players. Probability that Beena will beat Kuhu in 3 games out of 4 is 25%.

Reason (R): The probability of r successes in n trials, denoted by $P(X = r)$ is given by $P(X=r) = {^nC}_rp^rq^{n-r}, r = 0, 1, 2, ..., n$ where p denotes success and q denotes failure in each trial.

Select the correct answer from the options as given below.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

The correct answer is Option (1) → Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

Let Beena beats Kuhu be the success, then $p =\frac{1}{2}$

$⇒q=1-\frac{1}{2}=\frac{1}{2}$

Given $n = 4$

So, $P(X = 3) = {^4C}_3 (\frac{1}{2})^3.(\frac{1}{2})^1$

$= 4 ×\frac{1}{8}×\frac{1}{2}=\frac{1}{4}= 0.25$

∴ Assertion is true.

Also, Reason is true.

Reason is the correct explanation of Assertion.