Question:
A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is \( x \) and the probability that B will speak the truth is \( y \). A and B agree in a certain statement. The probability that the statement is true is
A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is \( x \) and the probability that B will speak the truth is \( y \). A and B agree in a certain statement. The probability that the statement is true is
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When working with independent events, multiply their individual probabilities and adjust for the condition that both agree.
Updated On: Jan 12, 2026
- \( x - y \)
- \( x + y \)
- \( 1 - x + y \)
- \( 1 - x + 2xy \)
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The Correct Option is D
Solution and Explanation
Step 1: Understand the probability of truth.
The probability that A and B agree on the truth is the product of their individual probabilities of speaking the truth, plus the probability that they both lie.
Step 2: Conclusion.
Thus, the probability that the statement is true is \( 1 - x + 2xy \).
Final Answer: \[ \boxed{1 - x + 2xy} \]
The probability that A and B agree on the truth is the product of their individual probabilities of speaking the truth, plus the probability that they both lie.
Step 2: Conclusion.
Thus, the probability that the statement is true is \( 1 - x + 2xy \).
Final Answer: \[ \boxed{1 - x + 2xy} \]
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