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?
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 \[ \frac{7}{10} \times \frac{4}{10} + \frac{3}{10} \times \frac{6}{10} \] \[ = \frac{28}{100} + \frac{18}{100} = \frac{46}{100} = \frac{23}{50} \]
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