k subsets of a set A= {1,2,3,...,n} are chosen at random with replacement. The probability that their intersection is

For k = 2. each element has four possibility and three out of four are favorable for the event.

 Hence required probability ${\left(\frac{3}{4}\right)}^{\mathrm{n}}$
For K 3, Probability that intersection is empty is ${\left(\frac{7}{8}\right)}^{\mathrm{n}}$
For k 3, Probability that intersection is singleton is $\frac{\mathrm{n}}{8}{\left(\frac{7}{8}\right)}^{\mathrm{n}-1}$