This question requires us to use the probability rule.

In the solution we must find P(both numbers are positive OR both numbers are negative)
This equals P(both numbers are positive) + P(both numbers are negative)

So, we still need to find the probability that the product is positive, but since this requires to find P(event A OR event B), we need to find the sum of the two probabilities to do so.

This is covered in the GMAT Prep Now video #7 - Applying the OR Rule

I hope that helps.

Cheers,
Brent

J N wrote:9/21?

Exacly

Here's the full solution.

P(positive product) = P(both numbers are positive OR both numbers are negative)
P(both numbers are positive) + P(both numbers are negative)

Now we'll calculate each part separately.

P(both numbers are positive)
P(both numbers are positive) = P(1st number is positive AND 2nd number is positive)
= P(1st number is positive) x P(2nd number is positive)
= (3/7) x (2/6)
= 1/7

P(both numbers are negative)
P(both numbers are negative) = P(1st number is negative AND 2nd number is negative)
= P(1st number is negative) x P(2nd number is negative)
= (4/7) x (3/6)
= 2/7

So, P(positive product) = 1/7 + 2/7
= 3/7

Cheers,
Brent

J N wrote:Luck or another way???

overall possible
7!/2!5! = 21

Pick 2 negatives
4!/2!2! = 6

Pick 2 positives
3!/2! = 3

9 possible ways to get positive/21 possible combinations

Great solution - perfect execution of counting techniques.

Cheers,
Brent

That's a good question.

I'd say that using probability rules is typically the faster approach, but there's also a matter of comfort level. If your counting techniques are strong (which they appear to be, judging from your post in this thread), then stick with that.

Cheers,
Brent