A) \[\frac{3}{20}\]
B) \[\frac{1}{5}\]
C) \[\frac{7}{20}\]
D) \[\frac{4}{5}\]
Correct Answer: C
Solution :
The probability of speaking truth by A, \[P(A)=\frac{4}{5}\] The probability of not speaking truth by \[A,P(\overline{A})=1-\frac{4}{5}=\frac{1}{5}\]. The probability of speaking truth by B, \[P(B)=\frac{3}{4}\]. The probability of not speaking truth of \[B,P(\overline{B})=\frac{1}{4}\] The probability that they contradict each other \[=P(\overline{A})\times P(\overline{B})+P(\overline{A})\times P(B)\] \[=\frac{4}{5}\times \frac{1}{4}+\frac{1}{5}\times \frac{3}{4}\] \[=\frac{1}{5}+\frac{3}{20}=\frac{7}{20}\]
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