Question

A speaks truth in 40% and B in 50% of the cases. The probability that they contradict each other while narrating some incident is:

• A. \( \frac{2}{3} \)
• B. \( \frac{1}{4} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{1}{3} \)

Hint:

To find the probability of contradictory events, consider all possible ways they can occur and add their probabilities.

Answer 1

The Correct Option is C

Step 1: Identify the probabilities. Probability that A speaks the truth = 0.40.
Probability that B speaks the truth = 0.50.
Probability that A lies = \( 1 - 0.40 = 0.60 \).
Probability that B lies = \( 1 - 0.50 = 0.50 \).
Step 2: Probability of contradicting each other. A and B will contradict each other in two cases:
Case 1: A speaks the truth and B lies.
Case 2: A lies and B speaks the truth.
The probability of each case is:
Case 1: \( 0.40 \times 0.50 = 0.20 \).
Case 2: \( 0.60 \times 0.50 = 0.30 \).
Thus, the total probability that they contradict each other is: \[ P({Contradiction}) = 0.20 + 0.30 = 0.50. \] Thus, the correct answer is: \[ \boxed{3}. \]