Subject

    Quantitative Aptitude

    Topic

    Probability

    A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

    ক)
    30/100
    খ)
    35/100
    গ)
    45/100
    ঘ)
    50/100

    Explanation

    Let   A = Event that A speaks the truth B = Event that B speaks the truth Then P(A) = 75/100 = 3/4 P(B) = 80/100 = 4/5 P(A-lie) = 1−341-\frac34 = 1/4 P(B-lie) = 1−451-\frac45 = 1/5 Now, A and B contradict each other =[A lies and B true] or [B true and B lies] = P(A).P(B-lie) + P(A-lie).P(B) = (35×15)+(14×45)=720\left(\frac35\times\frac15\right)+\left(\frac14\times\frac45\right)=\frac7{20} = (720×100)\left(\frac7{20}\times100\right) = 35%

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