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Probability

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by adi_800 » Sat Oct 08, 2011 11:40 pm
When a random experiment is conducted, the probability that event A occurs is 1/3. If the random experiment is conducted 5 independent times, what is the probability that event A occurs exactly twice?

A. 5/243
B. 25/243
C. 64/243
D. 80/243
E. 16/27

[spoiler]I was able to arrive till 8/243 but whats after tht? OA is D[/spoiler]
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by knight247 » Sat Oct 08, 2011 11:55 pm
Probability of Event Occurring is 1/3
Probability of Event NOT Occurring is 1-1/3=2/3

Let the Event occurring be represented by O and the Event NOT Occurring be represented by N
Our desired outcome is NNOOO and the Probability of this occurring is
(1/3)*(1/3)*(2/3)*(2/3)*(2/3)=8/243. You are correct till here.

However NNOOO can be arranged in 5!/(2!3!) Ways........(Permutation with repeating elements) Which equals 10. So the required probability is 10*8/243=[spoiler]80/243[/spoiler] Hence D
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