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Question
A speaks truth in 75% cases and B speaks truth in 80% cases. Probability that they contradict each other in a statement, is
Options
\[\frac{7}{20}\]
\[\frac{13}{20}\]
\[\frac{3}{5}\]
\[\frac{2}{5}\]
Solution
\[\frac{7}{20}\]
\[P\left( \text{ A speaks truth } \right) = 0 . 75\]
\[P\left( \text{ A lies } \right) = 1 - 0 . 75 = 0 . 25\]
\[P\left( \text{ B speaks truth } \right) = 0 . 8\]
\[P\left( \text{ B lies } \right) = 1 - 0 . 8 = 0 . 2\]
\[P\left( \text{ contradicting each other in a statement } \right) = P(A \text{ speaks truth and B lies } )+P\left( B\text{ speaks truth and A lies } \right)\]
\[ = 0 . 75 \times 0 . 2 + 0 . 8 \times 0 . 25\]
\[ = 0 . 15 + 0 . 2\]
\[ = 0 . 35\]
\[ = \frac{35}{100} = \frac{7}{20}\]
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