Probability Answers

Probability - Quant/Math - CAT 2008

Question 4 the day: June 23, 2003

The question for the day is from the topic of Probability.

An experiment succeeds twice as often as it fails. What is the probability that in the next 5 trials there will be four successes?

(1)	0			(2)	(2/3)^4
(3)	5*((2/3)^4)*(1/3)			(4)	((2/3)^4)*(1/3)

Correct Answer - (3)

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Solution:


An experiment succeeds twice as often as it fails.

i.e. the probability of its success is 2/3 and the probability of its failure is 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 5C4 ways = 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 1/3.

Hence, the required probability = 5*((2/3)^4)*(1/3)