The probability that A speaks truth is $$\frac{{3}}{{5}}$$ and that of B speaking truth is $$\frac{{4}}{{7}}$$. What is the probability that they agree in stating the same fact?

A. $$\frac{{18}}{{35}}$$

B. $$\frac{{12}}{{35}}$$

C. $$\frac{{17}}{{35}}$$

D. $$\frac{{19}}{{35}}$$

Answer: Option A

Solution(By Examveda Team)

If both agree stating the same fact, either both of them speak truth of both speak false.
∴ Probability
$$\eqalign{ & = \frac{3}{5} \times \frac{4}{7} + \frac{2}{5} \times \frac{3}{7} \cr & \, = \frac{{12}}{{35}} + \frac{6}{{35}} \cr & = \frac{{18}}{{35}} \cr} $$