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Probability Question- Trouble Using Alternative Method

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by onsamline » Thu Jul 04, 2013 8:18 pm
349. Company X has 800 employees and Company Y has 600 employees. Among these employees, there are 50 married couples, each consisting of an employee from Company X and an employee from Company Y. If 1 employee is to be selected at random from each company, what is the probability that the 2 employees selected will be a married couple?

A) 1/480,000
B) 1/9,600
C) 7/2,400
D) 1/192
E) 7/48



Correct Answer: B

I understand one way to solve it, (i.e. PROB of 1st Married Person from X (50/800) x PROB of 2nd Person in Couple from Y (1/600) = 1/9600), but I am having trouble trying to solve it via alternate method.

E.g. Couldn't I solve it 1 - PROB. of Selecting Non-married couple?

1 - (Non-married from X/800) x (Non-married coupling from Y/600) = ?

Therefore,
1 - ((750/800) x (600/600? since anyone I choose will not be part of a couple with company X?)

However, when I attempt this, I get a completely incorrect answer. Can someone please point out my flaw in reasoning?
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by Brent@GMATPrepNow » Thu Jul 04, 2013 8:33 pm
onsamline wrote:349. Company X has 800 employees and Company Y has 600 employees. Among these employees, there are 50 married couples, each consisting of an employee from Company X and an employee from Company Y. If 1 employee is to be selected at random from each company, what is the probability that the 2 employees selected will be a married couple?

A) 1/480,000
B) 1/9,600
C) 7/2,400
D) 1/192
E) 7/48

Correct Answer: B
First, a full solution.

P(select a married couple) = P(person selected from Company X is one of the 50 with spouse at Company Y AND person selected from Company Y is spouse of person selected from Company X)
= P(person selected from Company X is one of the 50 with spouse at Company Y) x P(person selected from Company Y is spouse of person already selected from Company X)
= (50/800) x (1/600)
= 1/9600
= B

Aside: Here's a similar problem: https://www.beatthegmat.com/probablility-qn-t45470.html

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Thu Jul 04, 2013 8:39 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Thu Jul 04, 2013 8:37 pm
onsamline wrote:349. Company X has 800 employees and Company Y has 600 employees. Among these employees, there are 50 married couples, each consisting of an employee from Company X and an employee from Company Y. If 1 employee is to be selected at random from each company, what is the probability that the 2 employees selected will be a married couple?

A) 1/480,000
B) 1/9,600
C) 7/2,400
D) 1/192
E) 7/48


1 - (Non-married from X/800) x (Non-married coupling from Y/600) = ?

Therefore,
1 - ((750/800) x (600/600? since anyone I choose will not be part of a couple with company X?)

However, when I attempt this, I get a completely incorrect answer. Can someone please point out my flaw in reasoning?
The problem with your solution is that there's more than 1 way for the 2 selected people to not be married.
1) neither person is one of the married people
2) person from X is married, but person from Y is not one of the 50 married people
3) person from Y is married, but person from X is not one of the 50 married people

Your solution accounts for case #1, but not cases #2 and #3

Your original solution was the best (fastest)

Cheers,
Brent
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by vipulgoyal » Thu Jul 04, 2013 9:11 pm
Brent, just out of curiosity I tried

1) neither person is one of the married people
2) person from X is married, but person from Y is not one of the 50 married people
3) person from Y is married, but person from X is not one of the 50 married people
got

55/64 + 11/192 + 5/64 = 1/192 (option D)

what i am missing ??
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by Brent@GMATPrepNow » Thu Jul 04, 2013 9:20 pm
vipulgoyal wrote:Brent, just out of curiosity I tried

1) neither person is one of the married people
2) person from X is married, but person from Y is not one of the 50 married people
3) person from Y is married, but person from X is not one of the 50 married people
got

55/64 + 11/192 + 5/64 = 1/192 (option D)

what i am missing ??
Actually, I gave you some bad advice. The 3 scenarios I mentioned still don't account for everything. We could also have
- person from X is married, but person from Y is not married to that person
- person from Y is married, but person from X is not married to that person

However, now that I think of it, we need to consider just two cases:
#1) person from X is married, but person from Y is not married to that person
#2) person from X is not married, and person from Y is anybody

Try these two cases, and I believe you'll reach the correct answer.

Cheers,
Brent
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by vipulgoyal » Thu Jul 04, 2013 9:47 pm
However, now that I think of it, we need to consider just two cases:
#1) person from X is married, but person from Y is not married to that person
#2) person from X is not married, and person from Y is anybody

Still

1 - 11/192 + 15/16
1 - 191/192 = 1/192
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by Brent@GMATPrepNow » Thu Jul 04, 2013 10:05 pm
#1. P( person from X is married, but person from Y is not married to that person) = (50/800)(599/600)
#2. P(person from X is not married, and person from Y is anybody) = (750/800)(600/600)

So, P(not married couple) = 1 - [(50/800)(599/600) + (750/800)(600/600)]
= 1/9600

As you can see, the original approach is MUCH better.

Cheers,
Brent
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by vipulgoyal » Thu Jul 04, 2013 10:22 pm
Thanks Brent, very well explained.
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