Company X has 800 employees and Company Y has 600 employees

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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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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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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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


Cheers,
Brent
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generis chetan2u here once we get 50/800*1/600 why do we not multiply this by 2? we could've first picked from company Y as well ie 50/600*1/800?

Probability of picking a married couple when you choose an employer from each company =

(# of favorable outcomes) / (every possible outcome in which one person from X is marched with another from Y)


# of favorable outcomes = 50 pairs of employers who make up a married couple


Total possible ways we can have an employee from X be chosen with an employer from Y = (each of the 800 employees at X) * (can be paired with any one of the 600 employees at Y) = (800) (600)


Answer

(50) / (800 * 600)

1 / 9,600

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