Question
A person X speaks the truth 4 out of 5 times and person Y speaks the truth 5 out of 6 times. What is the probability that they will contradict each other in stating the fact?
NDA
Mathematics
Probability
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 3/10
- B. 1/15
- C. 1/6
- D. 7/10
Answer
A. 3/10
Step-by-step solution
Let P(X) be the probability that person X speaks the truth and P(Y) be the probability that person Y speaks the truth. P(X) = 4 5 P(Y) = 5 6 The probability that X lies is P(X') = 1 - 4 5 = 1 5 . The probability that Y lies is P(Y') = 1 - 5 6 = 1 6 . They contradict each other when one speaks the truth and the other lies. The probability of this event is given by: P( contradiction ) = P(X)P(Y') + P(X')P(Y) P( contradiction ) = ( 4 5 ) ( 1 6 ) + ( 1 5 ) ( 5 6 ) P( contradiction ) = 4 30 + 5 30 = 9 30 = 3 10 Answer: 3/10
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