<p>The probability that \(A\) speaks truth is \(4/5\), while this probability for \(B\) is \(3/4\). The probability that they contradict each other when asked to speak on a fact is</p>
Step-by-Step Solution
Key Concept: They contradict when exactly one speaks truth and the other lies. Calculate P(A truth AND B lies) + P(A lies AND B truth) using independence.
<p><strong>Step 1:</strong> Identify when A and B contradict. They contradict when their statements are opposite—one tells truth and the other lies.</p><p><strong>Step 2:</strong> Set up the cases:</p><ul><li>P(A speaks truth) = 4/5, so P(A lies) = 1/5</li><li>P(B speaks truth) = 3/4, so P(B lies) = 1/4</li></ul><p><strong>Step 3:</strong> Calculate probability of contradiction:</p><p>P(Contradict) = P(A truth ∩ B lies) + P(A lies ∩ B truth)</p><p>Since A and B are independent:</p><p>P(Contradict) = (4/5)(1/4) + (1/5)(3/4)</p><p>P(Contradict) = 4/20 + 3/20 = 7/20</p><p>∴ Answer: <strong>7/20</strong></p>
Correct Answer: C