2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 are prime numbers between 1 to 60.

Total prime numbers = 17.

Total tickets = 60.

Number of ways to drawn 2 tickets from 60 tickets is n(s) \(= 60 C_2.\)

(i) Number of ways to drawn 2 tickets from tickets which numbered as prime numbers is \(n(E_1) = 17 C_2\)

\(\therefore\) Probability that both drawn tickets are prime numbers is \(p(E_1) = \frac{n(E_1)}{n(s)} = \frac{17\,C_2}{60\,C_2}\) \(= \cfrac{\frac{17 \times 16}{2!}}{\frac{60 \times 59}{2!}}\)

\(= \frac{17 \times 16}{60 \times 59} = \frac{17 \times 4}{15 \times 59}\) \(= \frac{68}{885}.\)

(ii) Number of ways to drawn 2 tickets from those tickets which numbered as non prime numbers is \(n(E_2) = 60 - 17 C_2 = 43 C_2.\)

\(\therefore\) Probability that none of the tickets has prime number is \(P(E_2) = \frac{n(E_2)}{n(s)}\) \(= \frac{43\, C_2}{60\, C_2}\) \(= \cfrac{\frac{43 \times 42}{2!}}{\frac{60 \times 59}{2!}}\)

\(= \frac{43 \times 42}{60 \times 59} = \frac{43 \times 21}{30 \times 59}\) \(= \frac{903}{1770}\)