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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?

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? Correct Answer $$\frac{{18}}{{35}}$$

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

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