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# If the probability of Sita getting selected to a school is

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Senior Manager
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If the probability of Sita getting selected to a school is [#permalink]

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13 Apr 2012, 15:35
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If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125

My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?
[Reveal] Spoiler: OA
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Re: If the probability of Sita getting selected to a school is [#permalink]

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13 Apr 2012, 15:54
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If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125

My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?

It's much better to calculate the probability of the opposite event, which would be that Sita will be rejected by all three schools, and subtract that value from 1: $$P=1-(\frac{4}{5})^3=\frac{61}{125}$$.

Direct approach:
The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:

1. She is selected by only one school: $$P(SRR)=\frac{3!}{2!}*\frac{1}{5}*\frac{4}{5}*\frac{4}{5}=\frac{48}{125}$$ (S stands for selected and R stands for rejected). We are multiplying by $$\frac{3!}{2!}$$, since SRR scenario can occur in several ways: SRR, RSR, RRS, (so $$\frac{3!}{2!}$$ is # of permutations of 3 letters SRR out of which 2 R's are identical);

2. She is selected by only two school: $$P(SSR)=\frac{3!}{2!}*\frac{1}{5}*\frac{1}{5}*\frac{4}{5}=\frac{12}{125}$$, the same reason of multiplying by $$\frac{3!}{2!}$$;

3. She is selected by all three school: $$P(SSS)=(\frac{1}{5})^3=\frac{1}{125}$$, we are not multiplying this time since SSS can occur only in one way.

So $$P=\frac{48}{125}+\frac{12}{125}+\frac{1}{125}=\frac{61}{125}$$.

Hope it's clear.
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Re: If the probability of Sita getting selected to a school is [#permalink]

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13 Apr 2012, 23:36
Bunuel wrote:
If the probability of Sita getting selected to a school is 20% and she applied to 3 schools. What is the probability that she will get selected in at least one school?

A. 24/125
B. 21/125
C. 61/125
D. 12/125
E. 18/125

My answer is : 1/5 *4/5*4/5+1/5*1/5*4/5+1/5*1/5*1/5 = 21/125

However if i go by another approach the answer is 1- 4/5 * 4/5*4/5 =61/125

What i am missing , Please comment?

It's much better to calculate the probability of the opposite event, which would be that Sita will be rejected by all three schools, and subtract that value from 1: $$P=1-(\frac{4}{5})^3=\frac{61}{125}$$.

Direct approach:
The probability that she will be selected by at least one school equals to the sum of the probabilities of the following three events:

1. She is selected by only one school: $$P(SRR)=\frac{3!}{2!}*\frac{1}{5}*\frac{4}{5}*\frac{4}{5}=\frac{48}{125}$$ (S stands for selected and R stands for rejected). We are multiplying by $$\frac{3!}{2!}$$, since SRR scenario can occur in several ways: SRR, RSR, RRS, (so $$\frac{3!}{2!}$$ is # of permutations of 3 letters SRR out of which 2 R's are identical);

2. She is selected by only two school: $$P(SSR)=\frac{3!}{2!}*\frac{1}{5}*\frac{1}{5}*\frac{4}{5}=\frac{12}{125}$$, the same reason of multiplying by $$\frac{3!}{2!}$$;

3. She is selected by all three school: $$P(SSS)=(\frac{1}{5})^3=\frac{1}{125}$$, we are not multiplying this time since SSS can occur only in one way.

So $$P=\frac{48}{125}+\frac{12}{125}+\frac{1}{125}=\frac{61}{125}$$.

Hope it's clear.

BB's answers are 99.99999 times crystal clear..

thanks for the explanation BB
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Harsha

Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat

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Re: If the probability of Sita getting selected to a school is [#permalink]

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22 Sep 2013, 21:01
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Re: If the probability of Sita getting selected to a school is [#permalink]

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21 Oct 2014, 15:05
Hello from the GMAT Club BumpBot!

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Re: If the probability of Sita getting selected to a school is [#permalink]

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12 Sep 2016, 06:03
Hello from the GMAT Club BumpBot!

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Re: If the probability of Sita getting selected to a school is   [#permalink] 12 Sep 2016, 06:03
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