If x is chosen at random from the set 1, 2, 3, 4 and y is to be chosen at random from the set 5, 6, 7, what is the probability that xy will be even?

Answer: Option D

S = {(1, 5), (1, 6), (1, 7), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 7), (4, 5), (4, 6), (4, 7)}
Total element n(S) = 12
xy will be even when even x or y or both will be even.
Events of x, y being even is E.
E = {(1, 6), (2, 5), (2, 6), (2, 7), (3, 6), (4, 5), (4, 6),(4, 7)}
n(E) = 8
So, Probability
$$\begin{array}{rl}& P=\frac{n(E)}{n(S)}\\ & P=\frac{8}{12}\\ & P=\frac{2}{3}\end{array}$$