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Concentration: , International Business
What is the probability P that A and B are both
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Updated on: 29 Jun 2021, 09:36
Updated on: 29 Jun 2021, 09:36
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Question Stats:
43% (02:26) correct
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What is the probability P that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
P |
26/165 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
Originally posted by COolguy101 on 27 Jun 2021, 06:52.
Last edited by KarunMendiratta on 29 Jun 2021, 09:36, edited 2 times in total.
Last edited by KarunMendiratta on 29 Jun 2021, 09:36, edited 2 times in total.
Edited by Carcass
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What is the probability P that A and B are both
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29 Jun 2021, 09:44
29 Jun 2021, 09:44
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kumarneupane4344 wrote:
What is the probability P that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
P |
26/165 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
We already have A and B, so we need to pick 38 more people from 100 - 2 = 98 people
This can be done in \(^{98}C_{38}\)
Total ways = \(^{100}C_{40}\)
P = \(\frac{^{98}C_{38}}{^{100}C_{40}}\)
P = \(\frac{98!}{(38!)(60!)} \frac{(40!)(60!)}{100!}\)
P = \(\frac{(98!)(40!)}{(38!)(100!)} = \frac{(40)(39)}{(100)(99)} = \frac{26}{165}\)
Hence, option C
Senior Manager
Joined: 23 Jan 2021
Posts: 294
Given Kudos: 81
Concentration: , International Business
Re: What is the probability P that A and B are both
[#permalink]
02 Jul 2021, 07:11
02 Jul 2021, 07:11
KarunMendiratta wrote:
kumarneupane4344 wrote:
What is the probability P that A and B are both selected when you select 40 people out of a group of 100 (A and B included)?
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
P |
26/165 |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D . The relationship cannot be determined from the information given.
We already have A and B, so we need to pick 38 more people from 100 - 2 = 98 people
This can be done in \(^{98}C_{38}\)
Total ways = \(^{100}C_{40}\)
P = \(\frac{^{98}C_{38}}{^{100}C_{40}}\)
P = \(\frac{98!}{(38!)(60!)} \frac{(40!)(60!)}{100!}\)
P = \(\frac{(98!)(40!)}{(38!)(100!)} = \frac{(40)(39)}{(100)(99)} = \frac{26}{165}\)
Hence, option C
Kudos!
