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.
Answer & explanation
Correct answer: option 1
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.