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?

General
1

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?

2

To find the probability that both A and B agree in stating the same fact, we can use the formula for the probability of the intersection of two independent events.

Let’s represent the event that A speaks truth as “A” and the event that B speaks truth as “B”. We want to find the probability that A and B both speak the same fact, which can be represented as P(A ∩ B).

If A and B are independent events, then the probability of the intersection P(A ∩ B) is equal to the product of their individual probabilities: P(A) * P(B).

Given that P(A) = 3/5 and P(B) = 4/7, we can calculate:

P(A ∩ B) = P(A) * P(B) = (3/5) * (4/7) = 12/35.

Therefore, the probability that A and B agree in stating the same fact is 12/35.