JEE Main & Advanced AIEEE Solved Paper-2004

  • question_answer The probability that A speaks truth is 4/5 while this probability for B is 3/4. The probability that they contradict each other when asked to speak on a fact, is

    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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