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If the probability of Sita getting selected to a school is

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If the probability of Sita getting selected to a school is [#permalink] New post 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?
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Re: If the probability of Sita getting selected to a school is [#permalink] New post 13 Apr 2012, 15:54
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vdadwal 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}.

Answer: C.

Hope it's clear.
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Re: If the probability of Sita getting selected to a school is [#permalink] New post 13 Apr 2012, 23:36
Bunuel wrote:
vdadwal 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}.

Answer: C.

Hope it's clear.


BB's answers are 99.99999 times crystal clear.. :)

thanks for the explanation BB
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Re: If the probability of Sita getting selected to a school is [#permalink] New post 22 Sep 2013, 21:01
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Re: If the probability of Sita getting selected to a school is   [#permalink] 22 Sep 2013, 21:01
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