Final answer:
To calculate the probability of A and B agreeing, we sum the probabilities of both telling the truth and both lying. This total probability is 18/35, which represents the chance that they agree on stating the same fact.
Step-by-step explanation:
The question is about calculating the probability that two people, A and B, will agree on stating the same fact, given that A speaks the truth with a probability of 3/5 and B with a probability of 4/7.
To find the probability that they agree, we need to consider two scenarios: both tell the truth, and both lie. The total probability of agreement is the sum of the probabilities of these two scenarios.
- The probability that both A and B tell the truth is (3/5) × (4/7) = 12/35.
- The probability that both A and B lie is (1 - 3/5) × (1 - 4/7) = (2/5) × (3/7) = 6/35.
Adding both probabilities gives us the total probability of agreement: 12/35 + 6/35 = 18/35.