A two digit number is formed from the digits 0, 1, 2, 3 without repetition. Find the probability that the number is (a) even (b) prime.

Q.21 A two digit number is formed from the digits 0, 1, 2, 3 without repetition. Find the probability that the number is (a) even (b) prime.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: (a) \(\dfrac{5}{9}\) (b) \(\dfrac{1}{3}\)

0 cannot be in the tens place, otherwise the number is not two digit.

S = {10, 12, 13, 20, 21, 23, 30, 31, 32}, n(S) = 9

(a) Even: units digit 0 or 2. A = {10, 12, 20, 30, 32}, n(A) = 5, \(P(A) = \dfrac{5}{9}\)

(b) Prime: check each number; 21 = 3 × 7 is not prime. B = {13, 23, 31}, n(B) = 3, \(P(B) = \dfrac{3}{9} = \dfrac{1}{3}\)

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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