Let p, q be chosen one by one from the set {1, √2 , √3, 2, e, π} with replacement. Now a circle is drawn taking (p, q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)

Question : Let p, q be chosen one by one from the set {1, √2 , √3, 2, e, π} with replacement. Now a circle is drawn taking (p, q) as its centre. Then the probability that at the most two rational points exist on the circle is (rational points are those points whose both the coordinates are rational)