Question
An urn contains 10 white and 5 red balls. If two balls are drawn at random, then what is the probability that both the balls are red?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 2/21
- B. 1/7
- C. 4/21
- D. 3/7
Answer
A. 2/21
Step-by-step solution
Total number of balls in the urn = 10 + 5 = 15 Number of ways to draw 2 balls from 15 balls = ^ 15 C_ 2 Number of ways to draw 2 red balls from 5 red balls = ^ 5 C_ 2 Required probability = ^ 5 C_ 2 ^ 15 C_ 2 ^ 5 C_ 2 = 5 4 2 = 10 ^ 15 C_ 2 = 15 14 2 = 105 Required probability = 10 105 = 2 21
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