Atal speaks the truth in 70% of the cases and George speaks the truth in 60% cases. In what percentage of cases are they likely to contradict each other in stating the same fact?
Step-by-step Solution:
They are likely to contradict each other in stating the same fact only when one speaks the truth and the other lies, so the required probability is \[ \frac{7}{10} \times \frac{4}{10} + \frac{3}{10} \times \frac{6}{10} \] \[ = \frac{28}{100} + \frac{18}{100} = \frac{46}{100} = \frac{23}{50} \]