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The probability that a speaks truth is 3/5 and that of b speaking truth is 4/7. what is the probability that they agree in stating the same fact?

a. 18/35
b. 12/35
c. 17/35
d. 19/35

User Flamemyst
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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.

User Daniel Stefaniuk
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