Set $$M=\{-6,-5,-4,-3,-2\}$$ and set $$N=\{-2,-1,0,1,2,3\}$$. Two integers are selected at random, one from set $$\mathrm{M} \&$$ the other from set N , we need to find the probability that the product of the two integers is negative.

Set $$M$$ \& set $$N$$ has 5 and 6 elements respectively, if one integer selected from set $M$ \& the other from set N , the total number of different combinations that can be formed will be $$5 \times 6=30$$.

Now, if we want the product of the integers selected to be negative, we would have to take exactly one of the two numbers negative.

As set $M$ doesn't have positive number, we can select only negative number from set $M$ in 6 ways and from set N only positive numbers need to selected and as there are only 3 positive numbers in set N , the positive number selection can be done in 3 ways, so total number of selections of the numbers from the two sets such that their product is negative is $$5 \times 3=15$$.

Prpbability $= \frac{15}{30}=\frac{1}{2}$