<p>\(A\) speaks truth in 60% cases and \(B\) speaks truth in 70% cases. The probability that they will say the same thing while describing a single event is</p>
Step-by-Step Solution
Key Concept: When two people describe the same event, they 'say the same thing' if both speak truth OR both lie together. Calculate P(both truth) + P(both lie) by treating their truth-speaking independently.
<p><strong>Step 1:</strong> Identify the two scenarios where they say the same thing:</p><ul><li>Both speak the truth</li><li>Both lie (speak falsehood)</li></ul><p><strong>Step 2:</strong> Calculate P(A speaks truth) = 0.6, so P(A lies) = 0.4</p><p>Calculate P(B speaks truth) = 0.7, so P(B lies) = 0.3</p><p><strong>Step 3:</strong> Since A and B are independent:</p><p>P(both speak truth) = 0.6 × 0.7 = 0.42</p><p>P(both lie) = 0.4 × 0.3 = 0.12</p><p><strong>Step 4:</strong> P(they say same thing) = P(both truth) + P(both lie)</p><p>= 0.42 + 0.12 = 0.54 = 54/100 = 27/50</p><p>∴ Answer: <strong>27/50 or 0.54</strong></p>
Correct Answer: B