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Bluelagoon
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If the probability of Sita getting selected to a school is 13 Apr 2012, 16:35
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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


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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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Bunuel
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If the probability of Sita getting selected to a school is 13 Apr 2012, 16:54
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vdadwal
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?
Show more

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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If the probability of Sita getting selected to a school is 14 Apr 2012, 00:36
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vdadwal
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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BB's answers are 99.99999 times crystal clear.. :)

thanks for the explanation BB
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If the probability of Sita getting selected to a school is 23 Jan 2018, 08:59
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Bluelagoon
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
Show more

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

Answer: C
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If the probability of Sita getting selected to a school is 22 Feb 2025, 12:02
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