A) \[3/20\]
B) \[4/5\]
C) \[9/20\]
D) \[7/20\]
Correct Answer: C
Solution :
Given, probability that A speaks truth \[P(A)=\frac{3}{5}\] \[\therefore \] Probability that A not speaks truth, \[P(\bar{A})\] \[=1-\frac{3}{5}=\frac{2}{5}\] Probability that B speaks the truth, \[P(B)=\frac{3}{4}\] \[\therefore \] Probability that B not speaks truth, \[P(\bar{B})=1-\frac{3}{4}\] \[=\frac{1}{4}\] Required probability \[=P(A)P(\bar{B})+P(\bar{A})P(B)\] \[=\frac{3}{5}\times \frac{1}{4}+\frac{2}{5}\times \frac{3}{4}=\frac{3}{20}+\frac{6}{20}=\frac{9}{20}\]
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