$A$ speaks truth in 60% cases and $B$ speaks truth in 70% cases. The probability that they will say the same thing while describing single event is:
Step-by-Step Solution
Key Concept: Two independent events produce the same statement when both speak truth OR both lie. Apply the addition rule: P(same) = P(both truth) + P(both lie) = P(A truth)·P(B truth) + P(A lie)·P(B lie) = (0.6)(0.7) + (0.4)(0.3).
Two people say the same thing when either both speak truth or both lie. The probability is $(0.6 imes 0.7) + (1 - 0.6)(1 - 0.7) = 0.42 + 0.12 = 0.54$.
Correct Answer: 2