# Moderate Probability Solved QuestionAptitude Discussion

 Q. An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?
 ✖ A. $0$ ✖ B. $\left(\frac{2}{3}\right)^4$ ✔ C. $5\times \left(\frac{2}{3}\right)^4\times \left(\frac{1}{3}\right)$ ✖ D. $\left(\frac{2}{3}\right)^4\times \left(\frac{1}{3}\right)$

Solution:
Option(C) is correct

An experiment succeeds twice as often as it fails.

i.e. the probability of its success is $\dfrac{2}{3}$ and the probability of its failure is $\dfrac{1}{3}$

In the next 5 trials the experiment needs to succeed in 4 out of the 5 trials.

4 out of the 5 trials in which it succeeds could be selected in $^5C_4=5$ ways.

And as 4 of them are successes, they have a probability of 2/3 and the one that is a failure will have a probability of

$\dfrac{1}{3}$

Hence, the required probability

$=5\times \left(\dfrac{2}{3}\right)^4\times \left(\dfrac{1}{3}\right)$