The total number of outcomes = 30.

(i) Let E₁ be the event of getting a number not divisible by 3.

out of these numbers, numbers divisible by 3 are 3,6,9,12,15,18,21,245,27 and 30.

number of favorable outcomes  = 30 - 10 = 20

Therefore P(getting a number not divisible by 3) = P(E₁) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_1}{number\,of\,all\,possible\,outcomes}\) = \(\frac{20}{30}\) = \(\frac{2}{3}\).

Thus, the probability that the number on the card is not divisible by 3 is \(\frac{2}{3}\).

(ii) Let E₁ be the event of getting a prime number greater than 7.

out of these numbers, prime numbers greater than 7 are 11,13,17,19,23 and 29.

number of favorable outcomes = 6

Therefore P(getting a prime number greater than 7) = P(E₂) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_2}{number\,of\,all\,possible\,outcomes}\) = \(\frac{6}{30}\) = \(\frac{1}{5}\).

Thus, the probability that the number on the card is a prime number greater than 7 is \(\frac{1}{5}\).

(iii) Let E₃ be the event of getting a number which is not a perfect square number.

out of these numbers, perfect square numbers are 1,4,9,16 and 25.

number of favorable outcomes = 30 - 5 = 25

Therefore P(getting non-perfect square number) = P(E₃) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_3}{number\,of\,all\,possible\,outcomes}\) = \(\frac{25}{30}\) = \(\frac{5}{6}\).

Thus, the probability that the number on the card is not a perfect square number is \(\frac{5}{6}\).