NDA Mathematics Question (2025) — Solution

Step-by-step solution

Total number of integers in the sample space, n(S) = 50. Let A be the event that the chosen integer is divisible by 5, and B be the event that it is divisible by 9. The number of integers divisible by 5 is n(A) = 10. The number of integers divisible by 9 is n(B) = 5. The number of integers divisible by both 5 and 9 (i.e., divisible by 45) is n(A B) = 1. The number of integers divisible by either 5 or 9 is given by: n(A B) = n(A) + n(B) - n(A B) = 10 + 5 - 1 = 14 The number of integers neither divisible by 5 nor 9 is: n(A' B') = n(S) - n(A B) = 50 - 14 = 36 The required probability is: P(A' B') = 36 50 = 18 25 Answer: 18/25