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Give that there are 5 married couples. If we select only 3 people out
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Updated on: 14 Sep 2019, 21:37
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Q. Given that there are 5 married couples. If we select only 3 people out of the 10, what is the probability that none of them are married to each other?
I want to solve this question using reverse probability approach, can someone post the solution pls.
Re: Give that there are 5 married couples. If we select only 3 people out
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02 Sep 2018, 12:17
Total ways to choose 3 out of 10 people is 10C3 = 120
Ways to choose 3 out of 10 where no 3 are married to each other = #ways to choose 3 out of 5 * 2^3 (as each chosen person can be replaced by his partner) = 5C3 × 8 = 80
Re: Give that there are 5 married couples. If we select only 3 people out
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02 Sep 2018, 17:08
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aggvipul wrote:
Q. Given that there are 5 married couples. If we select only 3 people out of the 10, what is the probability that none of them are married to each other?
I want to solve this question using reverse probability approach, can someone post the solution pls. OA - \(\frac{2}{3}\)
I don't think using the reverse probability(probability none are married = 1 - probabilty at least one pair is married) is the best approach. The reason for this is because we have to take into account the fact that there are multiple ways of getting a couple ---> pick 1 is married to pick 2, pick 2 is married to pick 3, pick 1 is married to pick 3.
Probability no couples = (Number of 3 person selections with no couples)/Total number of selections of 3 people from 10
Number of 3 person selections with no couples = (10 * 8 * 6)/3! ---->80 -Note: We have to divide by 3! to get rid of repeats(ie ABC is the same team as BAC)
Total number of selections of 3 people from 10 ----> 10C3 = 10!/(7! * 3!) = 120
80/120 = 2/3
_________________
Adam Rosman, MD University of Chicago Booth School of Business, Class of 2020 adam@alldaytestprep.com
Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock. https://www.alldaytestprep.com
Re: Give that there are 5 married couples. If we select only 3 people out
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03 Sep 2018, 00:31
arosman wrote:
aggvipul wrote:
Q. Given that there are 5 married couples. If we select only 3 people out of the 10, what is the probability that none of them are married to each other?
I want to solve this question using reverse probability approach, can someone post the solution pls. OA - \(\frac{2}{3}\)
I don't think using the reverse probability(probability none are married = 1 - probabilty at least one pair is married) is the best approach. The reason for this is because we have to take into account the fact that there are multiple ways of getting a couple ---> pick 1 is married to pick 2, pick 2 is married to pick 3, pick 1 is married to pick 3.
Probability no couples = (Number of 3 person selections with no couples)/Total number of selections of 3 people from 10
Number of 3 person selections with no couples = (10 * 8 * 6)/3! ---->80 -Note: We have to divide by 3! to get rid of repeats(ie ABC is the same team as BAC)
Total number of selections of 3 people from 10 ----> 10C3 = 10!/(7! * 3!) = 120
80/120 = 2/3
Hi arosman while I agree that reverse probability approach may not be the best here but as mentioned in my post the purpose to get the answer through reverse probability is to learn the concept more thoroughly. bb can you pls help out here
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Re: Give that there are 5 married couples. If we select only 3 people out
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03 Sep 2018, 17:35
aggvipul wrote:
arosman wrote:
aggvipul wrote:
Q. Given that there are 5 married couples. If we select only 3 people out of the 10, what is the probability that none of them are married to each other?
I want to solve this question using reverse probability approach, can someone post the solution pls. OA - \(\frac{2}{3}\)
I don't think using the reverse probability(probability none are married = 1 - probabilty at least one pair is married) is the best approach. The reason for this is because we have to take into account the fact that there are multiple ways of getting a couple ---> pick 1 is married to pick 2, pick 2 is married to pick 3, pick 1 is married to pick 3.
Probability no couples = (Number of 3 person selections with no couples)/Total number of selections of 3 people from 10
Number of 3 person selections with no couples = (10 * 8 * 6)/3! ---->80 -Note: We have to divide by 3! to get rid of repeats(ie ABC is the same team as BAC)
Total number of selections of 3 people from 10 ----> 10C3 = 10!/(7! * 3!) = 120
80/120 = 2/3
Hi arosman while I agree that reverse probability approach may not be the best here but as mentioned in my post the purpose to get the answer through reverse probability is to learn the concept more thoroughly. bb can you pls help out here
Start at highest level possible.
Probability no couples picked + probability at least one couple picked = 1
Therefore -----> probability no couples picked = 1 - probability at least one couple picked
Since only three people are picked total, there is no way to select more than one couple. Therefore ---> probability at least one couple picked = probability exactly one couple picked
Probability exactly one couple picked = probability picks 1 & 2 are a couple + probability picks 1 & 3 are a couple + probability picks 2 & 3 are a couple
Since all 3 of these options are going to have the same probability we can just think of this as ---> probability exactly one couple picked = 3 * probability picks 1 & 2 are a couple
Imagine we have 3 slots.
Slot 1: Slot 1 can be any person as long as slot two is that person's partner. Probability of selecting any person is just 10/10 = 1
Slot 2: There are nine people left but only 1 of them is Slot 1's partner. Therefore probability here is 1/9
Slot 3: There are 8 people left and since we already have out couple any 8 of them can be selected. 8/8 = 1
Therefore, the exact probability of this exact sequence(Partner 1 ---> Partner 2 ---> Anybody else) is 1 * 1/9 * 1 = 1/9.
Accounting for the 3 different scenarios ------> Probability at least one couple = 3 * 1/9 = 1/3
Probability no couples = 1 - probability at least one couple = 1 - 1/3 = 2/3
Lemme know if you have any questions!
Best, Adam
_________________
Adam Rosman, MD University of Chicago Booth School of Business, Class of 2020 adam@alldaytestprep.com
Unlimited private GMAT Tutoring in Chicago for less than the cost a generic prep course. No tracking hours. No watching the clock. https://www.alldaytestprep.com
Re: Give that there are 5 married couples. If we select only 3 people out
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05 Nov 2018, 12:48
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Total number of ways of choosing 3 people is 10C3. Total number of ways of picking 3 couples out of 5 couples is 5C3. Now number of ways of picking one couple out of three couple is 2C1 X 2C1 X2C1. So, probability of picking no married couples is 5C3(2C1)^3 / 10C3 = 2/3
Re: Give that there are 5 married couples. If we select only 3 people out
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25 Nov 2019, 10:23
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