Final answer:
The probability that person A speaks the truth while person B lies is about 33%, which is closest to option A, about 32%.
Step-by-step explanation:
The question is asking us to find the probability that person A speaks the truth while person B lies. Person A speaks the truth 58% of the time (P(A) = 0.58), and person B speaks the truth 43% of the time (P(B) = 0.43). However, we are interested in the probability that person B lies, which is the complement of person B speaking the truth, so we calculate P(B') = 1 - P(B) = 1 - 0.43 = 0.57.
The probability that A speaks the truth and B lies simultaneously is then found by multiplying these individual probabilities since they are independent events:
P(A and B') = P(A) × P(B') = 0.58 × 0.57 ≈ 0.3306, or about 33%.
The correct answer would be closest to option A, about 32%.