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