Two numbers are selected together from 1, 2, 3, 4, 5. Find the probability that (a) their sum is even (b) their product is odd.

Q.23 Two numbers are selected together from 1, 2, 3, 4, 5. Find the probability that (a) their sum is even (b) their product is odd.

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

1 answer

Best answer

Answer: (a) \(\dfrac{2}{5}\) (b) \(\dfrac{3}{10}\)

The numbers are chosen together, so order does not matter.

S = {(1,2), (1,3), (1,4), (1,5), (2,3), (2,4), (2,5), (3,4), (3,5), (4,5)}, n(S) = 10

(a) Sum is even when both are odd or both are even. A = {(1,3), (1,5), (3,5), (2,4)}, n(A) = 4, \(P(A) = \dfrac{4}{10} = \dfrac{2}{5}\)

(b) Product is odd only when both numbers are odd. B = {(1,3), (1,5), (3,5)}, n(B) = 3, \(P(B) = \dfrac{3}{10}\)

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

Was this answer helpful?