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A speaks truth in 75% of cases and B in 80% of cases. In what percent of cases are they likely to contradict each other in narrating the same event?
Answer & Solution
Correct Answer:
Option
A
Different possible cases of contradiction,
A speaks truth and B does not speaks truth.
Or, A does not speak truth and B speaks truth.
$$\eqalign{ & = \left( {\frac{3}{4} \times \frac{1}{5}} \right) + \left( {\frac{1}{4} \times \frac{4}{5}} \right) \cr & = \frac{3}{{20}} + \frac{4}{{20}} \cr & = \frac{7}{{20}} \cr & = 35\% \cr} $$
A speaks truth and B does not speaks truth.
Or, A does not speak truth and B speaks truth.
$$\eqalign{ & = \left( {\frac{3}{4} \times \frac{1}{5}} \right) + \left( {\frac{1}{4} \times \frac{4}{5}} \right) \cr & = \frac{3}{{20}} + \frac{4}{{20}} \cr & = \frac{7}{{20}} \cr & = 35\% \cr} $$
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