Probability of matched couples

[Sagitha]

Exactly 60 couples (male-female) are enrolled in a university program. If all the female
spouses are in the undergraduate program comprising 700 students, and all the male
spouses in the graduate program comprising 300 students, and if one person is to be
randomly drawn from each of the two programs, what is the probability that a matched

couple was picked?
answer is 60/700 * 1/300 and the reasoning given is that the probability of picking a married person from the undergraduate class is 60/700 and then for that person picking the person married to this person from the other class is 1/300. Fair enough. But why should we also consider the other way also ? That is, what if we first select 60/300 from the graduate class and then for that person select 1/700 from the undergraduate class?

[xperience]

Originally Posted by Sagitha

Exactly 60 couples (male-female) are enrolled in a university program. If all the female

spouses are in the undergraduate program comprising 700 students, and all the male
spouses in the graduate program comprising 300 students, and if one person is to be
randomly drawn from each of the two programs, what is the probability that a matched

couple was picked?
answer is 60/700 * 1/300 and the reasoning given is that the probability of picking a married person from the undergraduate class is 60/700 and then for that person picking the person married to this person from the other class is 1/300. Fair enough. But why should we also consider the other way also ? That is, what if we first select 60/300 from the graduate class and then for that person select 1/700 from the undergraduate class?

A very valid question indeed. Just one query though. Among the answer choices, is 60/300*1/700 given as one of the answer choices?
My guess is that it wouldn't have been given.

But if it is, then lord help me out.

[parajulibharat]

Sagitha,

Doesn't that produces the same result?

60/300 * 1/700 = 60/700 * 1/300

[vineejay]

Yes it comes to the same answer both ways.

[ss1]

shouldnt we reduce the number by 1 fr the second pick? for eg, 60/700 then 1/299?