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?

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? Correct Answer $$\frac{{2}}{{3}}$$

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
$$\eqalign{ & P = \frac{{n(E)}}{{n(S)}} \cr & P = \frac{8}{{12}} \cr & P = \frac{2}{3} \cr} $$
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