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. \( x - y \)
• B. \( x + y \)
• C. \( 1 - x + y \)
• D. \( 1 - x + 2xy \)

Hint:

When working with independent events, multiply their individual probabilities and adjust for the condition that both agree.

Answer 1

The Correct Option is D

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: \[ \boxed{1 - x + 2xy} \]