In a Binomial distribution, the probability of getting a success is \(\displaystyle\frac{3}{4}\) and the variance is \(\displaystyle\frac{3}{8}\) then the probability of no success is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{1}{16}\)
For a binomial distribution with n trials, the variance is npq.
\( \displaystyle p = \frac{3}{4}, \quad q = 1 - p = \frac{1}{4} \)
\( \displaystyle n \times \frac{3}{4} \times \frac{1}{4} = \frac{3}{8} \)
\( \displaystyle \frac{3n}{16} = \frac{3}{8} \)
\(n = 2\)
No success means all n trials fail:
\( \displaystyle P(X = 0) = q^{n} = \left(\frac{1}{4}\right)^{2} = \frac{1}{16} \)