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 wha...........

Explanation:

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

P(E)=n(E)/n(S)=8/12 = 2/3

Hence, option 2 is the correct answer.