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Company X has 800 employees and Company Y has 600 employees

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Company X has 800 employees and Company Y has 600 employees  [#permalink]

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New post 25 Aug 2018, 10:55
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Question Stats:

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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) \(\frac{1}{480000}\)

(B) \(\frac{1}{9600}\)

(C) \(\frac{7}{2400}\)

(D) \(\frac{1}{192}\)

(E) \(\frac{7}{48}\)
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Company X has 800 employees and Company Y has 600 employees  [#permalink]

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New post 25 Aug 2018, 11:42
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Bismarck wrote:
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) \(\frac{1}{480000}\)

(B) \(\frac{1}{9600}\)

(C) \(\frac{7}{2400}\)

(D) \(\frac{1}{192}\)

(E) \(\frac{7}{48}\)

The trick to solving this problem is to notice that we account for 50 married couples (100 total persons, 50 in each company) only once.

Among a total of 1,400 employees there are 50 married couples.
Each couple consists of one employee from company X and another from company Y.

We find the probability of selecting a married employee from the first company.

After selecting the first employee, however, the next pick is limited.

She IS married to only ONE person from the second company. There are not 50 possibilities for the second pick; there is only one possibility.

P(married employee, M) on
First pick = \(\frac{50}{800}\)

P(selecting M's spouse) from second company
Second pick = \(\frac{1}{600}\)

Multiply

\((\frac{50}{800}*\frac{1}{600})=\frac{50}{480,000}=\frac{1}{9,600}\)

Answer B
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Re: Company X has 800 employees and Company Y has 600 employees  [#permalink]

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New post 28 Nov 2019, 17:45
Bismarck wrote:
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) \(\frac{1}{480000}\)

(B) \(\frac{1}{9600}\)

(C) \(\frac{7}{2400}\)

(D) \(\frac{1}{192}\)

(E) \(\frac{7}{48}\)


The probability of selecting a married person from company X = 50/800. The probability of selecting that person’s partner in Company Y is 1/600. Therefore, the overall probability of selecting a married couple is 50/800 * 1/600 = 1/800 * 1/12 = 1/9600.

Answer: B
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Re: Company X has 800 employees and Company Y has 600 employees  [#permalink]

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New post 29 Nov 2019, 12:29
Bismarck wrote:
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) \(\frac{1}{480000}\)

(B) \(\frac{1}{9600}\)

(C) \(\frac{7}{2400}\)

(D) \(\frac{1}{192}\)

(E) \(\frac{7}{48}\)


We want to find the probability of randomly selecting a married couple. We can start from the probability of randomly selecting one person from Company X that is married, then find the probability of selecting that person's partner from company Y. Multiplying these will give the probability of selecting a married couple. That is 50/800 * 1/600 = 1/800 * 1/12 = 1*9600.

Ans: B
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Re: Company X has 800 employees and Company Y has 600 employees  [#permalink]

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New post 15 Jan 2020, 15:38
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Bismarck wrote:
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) \(\frac{1}{480000}\)

(B) \(\frac{1}{9600}\)

(C) \(\frac{7}{2400}\)

(D) \(\frac{1}{192}\)

(E) \(\frac{7}{48}\)


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


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Brent
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Re: Company X has 800 employees and Company Y has 600 employees   [#permalink] 15 Jan 2020, 15:38
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