In 3 trials of a binomial distribution, the probability of 2 successes is 9 times the probability of 3 successes, then the probability of success in each trial is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( \displaystyle\frac{1}{4} \)
With n = 3, the binomial probabilities are
\( \displaystyle P(X=2)=3p^{2}q \)
\( \displaystyle P(X=3)=p^{3} \)
Using the given condition:
\( \displaystyle 3p^{2}q=9p^{3} \)
\( \displaystyle q=3p \)
\( \displaystyle 1-p=3p \)
\( \displaystyle p=\frac{1}{4} \)