J & K CET Engineering J and K - CET Engineering Solved Paper-2014

  • question_answer The probability that A speaks the  truth is \[3\text{ }/5\] and probability that B speaks the truth is\[3\text{ }/4\] Find the probability that they contradict each other when; asked to speak a fact.

    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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