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Manager  Joined: 21 Jan 2010
Posts: 237
If the probability of Sita getting selected to a school is  [#permalink]

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10 00:00

Difficulty:   15% (low)

Question Stats: 76% (01:29) correct 24% (01:57) wrong based on 152 sessions

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Re: If the probability of Sita getting selected to a school is  [#permalink]

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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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Joined: 25 Feb 2010
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Re: If the probability of Sita getting selected to a school is  [#permalink]

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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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Joined: 04 Mar 2011
Posts: 2815
Re: If the probability of Sita getting selected to a school is  [#permalink]

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Bluelagoon 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

We can use the equation:

P(selected into at least 1 school) = 1 - P(selected to no schools)

P(selected to no schools) = 4/5 x 4/5 x 4/5 = 64/125

Thus,

P(selected into at least 1 school) = 1 - 64/125 = 61/125

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

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_________________ Re: If the probability of Sita getting selected to a school is   [#permalink] 10 Jul 2019, 04:41
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