Question

The probability that A speaks truth is 75\% and the probability that B speaks truth is 80\%. The probability that they contradict each other when asked to speak on a fact is:

• A. \( \frac{3}{20} \)
• B. \( \frac{4}{20} \)
• C. \( \frac{7}{20} \)
• D. \( \frac{5}{20} \)

Hint:

When two events contradict, compute the probability of each contradicting scenario separately and sum them.

Answer 1

The Correct Option is C

Step 1: Define probabilities \[ P(A) = 0.75, \quad P(B) = 0.80. \] Probability of lying: \[ P(A') = 1
- 0.75 = 0.25, \quad P(B') = 1
- 0.80 = 0.20. \] Step 2: Compute cases where they contradict each other Contradiction occurs in two scenarios: 1. A speaks truth and B lies: \( P(A) P(B') = 0.75 \times 0.20 = 0.15 \). 2. A lies and B speaks truth: \( P(A') P(B) = 0.25 \times 0.80 = 0.20 \). Total probability of contradiction: \[ 0.15 + 0.20 = 0.35 = \frac{7}{20}. \]