SOLUTION: If two numbers chosen from [-2011, 2012] are multiplied, find the probability that their product is greater than zero.

[-2011, 2012]

There are 2012 positive numbers, and 2011 negative numbers, and 1 zero.

So there are 2012+2011+1 or 4024 numbers to choose from.

We have to choose a pair of positive numbers or a pair of negative numbers.

If we choose the numbers with replacement:

P[(positive 1st AND positive 2nd) OR (negative 1st AND negative 2nd)] =

P(positive 1st)×P(positive 2nd) + P(negative 1st)×P(negative 2nd)

If the choosing of the numbers is done with replacement

× + ×

which works out to be  = .4997515528

If the choosing of the numbers is done without replacement

× + ×

which works out to be .4996272675

Edwin