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

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Senior Manager
Joined: 21 Jan 2010
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If the probability of Sita getting selected to a school is [#permalink]  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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Joined: 02 Sep 2009
Posts: 31356
Followers: 5367

Kudos [?]: 62601 [5] , given: 9457

Re: If the probability of Sita getting selected to a school is [#permalink]  13 Apr 2012, 15:54
5
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Expert's post
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.
_________________
Manager
Status: I will not stop until i realise my goal which is my dream too
Joined: 25 Feb 2010
Posts: 235
Schools: Johnson '15
Followers: 2

Kudos [?]: 42 [0], given: 16

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

Regards,
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

Satyameva Jayate - Truth alone triumphs

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Joined: 09 Sep 2013
Posts: 8244
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Kudos [?]: 111 [0], given: 0

Re: If the probability of Sita getting selected to a school is [#permalink]  22 Sep 2013, 21:01
Hello from the GMAT Club BumpBot!

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GMAT Club Legend
Joined: 09 Sep 2013
Posts: 8244
Followers: 420

Kudos [?]: 111 [0], given: 0

Re: If the probability of Sita getting selected to a school is [#permalink]  21 Oct 2014, 15:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: If the probability of Sita getting selected to a school is   [#permalink] 21 Oct 2014, 15:05
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