Given that x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7} and we need to find what is the probability that xy will be even

We know that Total Probability is always equal to 1

=> P(Odd) + P(Even) = 1
=> P(Even) = 1 - P(Odd)

To get xy as odd we need to have all of them as odd.
=> P(xy = Odd) = P(x = odd) * P(y = odd) = \(\frac{2}{4}\) * \(\frac{2}{3}\)

(Because for x we have two choices (1,3) to get odd out of 4, for y we have two choices (5,7) to get odd out of 3)

= \(\frac{1}{3}\)

=> P(Even) = 1 - P(Odd) = 1 - \(\frac{1}{3}\) = \(\frac{3 - 1}{3}\) = \(\frac{2}{3}\)

So, Answer will be D.
Hope it helps!