A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a - (1) prime number (2) multiple of 4 (3) multiple of 11.

Answer: (1) 3/10 (2) 3/10 (3) 1/5

Tens digit: 1, 2, 3, 4 (not 0); units digit: any of 0 to 4. So n(S) = \(4 \times 5 = 20\).

S = {10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44}

(1) Primes: 11, 13, 23, 31, 41, 43 (6 numbers). \( P = \frac{6}{20} = \frac{3}{10} \)

(2) Multiples of 4: 12, 20, 24, 32, 40, 44 (6 numbers). \( P = \frac{6}{20} = \frac{3}{10} \)

(3) Multiples of 11: 11, 22, 33, 44 (4 numbers). \( P = \frac{4}{20} = \frac{1}{5} \)