Probability
Aptitude

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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)$

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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

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


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