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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: i. prime number. ii. multiple of 4. iii multiple of 11. Select the correct answer from above options

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Sample space (S) = {10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44} ∴ n(S) = 20 i. Let A be the event that the number so formed is a prime number. ∴ A = {11, 13, 23, 31, 41, 43} ∴ n(A) = 6 ii. Let B be the event that the number so formed is a multiple of 4. ∴ B = {12, 20, 24, 32, 40, 44} ∴ n(B) = 6 iii. Let C be the event that the number so formed is a multiple of 11. ∴ C = {11, 22, 33, 44} ∴ n(C) = 4

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