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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 |
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(2) |
(2/3)^4 |
| (3) |
5*((2/3)^4)*(1/3) |
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(4) |
((2/3)^4)*(1/3) |
Correct Answer - (3)
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)
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