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AnirudhTiwari
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Confusion regarding a probability question 12 Dec 2019, 04:58
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Company A has 400 employees and company B has 500 employees. Among these employees, there are 50 married couples, each consisting of an employee from A and employee from B. If 1 employee is selected at random from each company, what is the probability that that the two employees selected would be a married couple?

I solved this question by calculating P(Picking a married person in company A)*P(picking the corresponding spouse in company B) + P(Picking a married person in company B)*P(Picking the corresponding spouse in A) = (50/400)*(1/500) + (50/500)*(1/400) = 1/2000.

But the answer provided by CrackVerbal is 1/40000. This is Question 6 on Application Videos of Probability. Can someone please clarify this?


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Anirudh
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Confusion regarding a probability question 12 Dec 2019, 05:54
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AnirudhTiwari
Company A has 400 employees and company B has 500 employees. Among these employees, there are 50 married couples, each consisting of an employee from A and employee from B. If 1 employee is selected at random from each company, what is the probability that that the two employees selected would be a married couple?

I solved this question by calculating P(Picking a married person in company A)*P(picking the corresponding spouse in company B) + P(Picking a married person in company B)*P(Picking the corresponding spouse in A) = (50/400)*(1/500) + (50/500)*(1/400) = 1/2000.

But the answer provided by CrackVerbal is 1/40000. This is Question 6 on Application Videos of Probability. Can someone please clarify this?


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Anirudh
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Highlighted portion is wrong..

The highlighted portion is just repeating what you have already found in the first term..
answer will be either (50/400)*(1/500) or (50/500)*(1/400)
Say A and B are one of the couple. You cannot have A as part of 400 and B as part of 500 and then B as part of 400 and A as part of 500 .
Because A will always be in one of the group and B will always be in th eother group.
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AnirudhTiwari
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Confusion regarding a probability question 12 Dec 2019, 06:55
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AnirudhTiwari
Company A has 400 employees and company B has 500 employees. Among these employees, there are 50 married couples, each consisting of an employee from A and employee from B. If 1 employee is selected at random from each company, what is the probability that that the two employees selected would be a married couple?

I solved this question by calculating P(Picking a married person in company A)*P(picking the corresponding spouse in company B) + P(Picking a married person in company B)*P(Picking the corresponding spouse in A) = (50/400)*(1/500) + (50/500)*(1/400) = 1/2000.

But the answer provided by CrackVerbal is 1/40000. This is Question 6 on Application Videos of Probability. Can someone please clarify this?


Thanks
Anirudh

Highlighted portion is wrong..

The highlighted portion is just repeating what you have already found in the first term..
answer will be either (50/400)*(1/500) or (50/500)*(1/400)
Say A and B are one of the couple. You cannot have A as part of 400 and B as part of 500 and then B as part of 400 and A as part of 500 .
Because A will always be in one of the group and B will always be in th eother group.
Show more


This makes perfect sense. Thanks for the help! :)
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Confusion regarding a probability question 12 Dec 2019, 16:42
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AnirudhTiwari
Company A has 400 employees and company B has 500 employees. Among these employees, there are 50 married couples, each consisting of an employee from A and employee from B. If 1 employee is selected at random from each company, what is the probability that that the two employees selected would be a married couple?

I solved this question by calculating P(Picking a married person in company A)*P(picking the corresponding spouse in company B) + P(Picking a married person in company B)*P(Picking the corresponding spouse in A) = (50/400)*(1/500) + (50/500)*(1/400) = 1/2000.

But the answer provided by CrackVerbal is 1/40000. This is Question 6 on Application Videos of Probability. Can someone please clarify this?


Thanks
Anirudh
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Probability = 50/500 * 1/400 or 50/400* 1/500 = 1/4000
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Confusion regarding a probability question 13 Dec 2019, 01:59
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AnirudhTiwari
Company A has 400 employees and company B has 500 employees. Among these employees, there are 50 married couples, each consisting of an employee from A and employee from B. If 1 employee is selected at random from each company, what is the probability that that the two employees selected would be a married couple?

I solved this question by calculating P(Picking a married person in company A)*P(picking the corresponding spouse in company B) + P(Picking a married person in company B)*P(Picking the corresponding spouse in A) = (50/400)*(1/500) + (50/500)*(1/400) = 1/2000.

But the answer provided by CrackVerbal is 1/40000. This is Question 6 on Application Videos of Probability. Can someone please clarify this?


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Anirudh
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Hello Anirudh,

As the other experts have already highlighted on their posts, you only need to select the respective halves of the couple from each company only once.

Selecting one person belonging to the couple from, say company A can happen in 50 ways. Therefore, probability = \(\frac{50}{400}\).

Selecting the other person belonging to the couple from company B can happen in only 1 way. Probability = \(\frac{1}{500}\).

You do not have to double the result since the same person cannot be in both the companies at the same time.
The required probability = \(\frac{50}{400}\) * \(\frac{1}{500}\) = \(\frac{1}{4000}\).

Just wanted to clarify that the answer is given as \(\frac{1}{4000}\) and not as \(\frac{1}{40000}\).
Hope that helps!