Question

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?

Answer 1

The probability that they agreeing the same fact will be

P(a speaks truth) *P(b speaks truth)

3/5*4/7= 12/35

Answer 2

Answer:  The required probability is $\dfrac{12}{35}.$

Step-by-step explanation:  Given that the probability that A speaks truth is $\dfrac{3}{5}$ and that of B speaking truth is $\dfrac{4}[7}$.

We are to find the probability that A and B agree in stating the same fact.

Let E and F denotes the events that A speaks truth ans B speaks truth respectively.

Then, according to the given information, we have

$P(E)=\dfrac{3}{5},\\\\\\P(F)=\dfrac{4}{7}.$

Since A and B are independent events, so the probability that A and B agree in stating the same fact is given by

$P(A\cap B)\\\\=P(A)\times P(B)\\\\\\=\dfrac{3}{5}\times\dfrac{4}{7}\\\\\\=\dfrac{12}{35}.$

Thus, the required probability is $\dfrac{12}{35}.$