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 \(= \frac{15}{30}=\frac{1}{2}\)