Two statements are given, one labelled Assertion (A) and the other labelled Reason (R).
Assertion (A): A coin is biased such that head is two times likely to occur as tail. If the coin is tossed 4 times, then the variance of number of heads is $\frac{8}{9}$.
Reason (R): Variance of binomial distribution = $\sqrt{npq}$ where n = number of trails; p = probability of success and q = probability of failure.
Select the correct answer from the options given below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (1) → Assertion (A) is true, but Reason (R) is false.
Given $P(H) = 2 P(T)$
Also, $P(H) + P(T) = 1$
$⇒2 P(T) + P(T) = 1$
$⇒P(T) = \frac{1}{3}$ and $P(H) = 2×\frac{1}{3}=\frac{2}{3}$
Let getting head be the success, then $p =\frac{2}{3}$ and $q=\frac{1}{3},n=4$
So, variance = $npq$
$=4×\frac{2}{3}×\frac{1}{3}=\frac{8}{9}$
∴ Assertion is true.
Reason is false.