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    Subject

    Quantitative Aptitude

    Topic

    Probability

    The probabilities that A and B will tell the truth are 2 / 3 and 4 / 5 respectively . What is the probability that they agree with each other ?

    ক)
    3/5
    খ)
    1/3
    গ)
    2/5
    ঘ)
    3/4

    Explanation

    Let A be the event of A will tell truth. B be the event of B tell truth P(A)=23,P(Ac)=1−P(A)=13P(A)=\frac23,P(A^c)=1-P(A)=\frac13 P(B)=45,P(Bc)=1−P(B)=15P(B)=\frac45,P(B^c)=1-P(B)=\frac15 When both agree then they say true or they say false together, that is A∩B  or  Ac∩BcA\cap B\;or\;A^c\cap B^c Also these events will be mutually exclusive : P(A∩B)+P(Ac∩Bc)=P(A)P(B)P(C)=23×45+13×15=35P(A\cap B)+P(A^c\cap B^c)=P(A)P(B)P(C)=\frac23\times\frac45+\frac13\times\frac15=\frac35

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