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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 45

  • question_answer
    A candidate has to reach the examination centre in time. Probability of him going by bus or scooter or by other means of transport are \[\frac{3}{10},\frac{1}{10},\frac{3}{5}\] respectively. The probability that he will be late is \[\frac{1}{4}\] and \[\frac{1}{3}\] respectively, if he travels by bus or scooter. But he reaches in time if the uses any mode of transport. He reached late at the centre. The probability that he travelled by bus is -

    A) \[\frac{1}{9}\]              

    B)        \[\frac{2}{13}\]

    C) \[\frac{9}{13}\] 

    D)        None of these

    Correct Answer: C

    Solution :

    [c] Let A, B, C be the events of candidate going by bus, scooter and other means of transport. Let E be the event of getting late. \[P(A)=\frac{3}{10},P(B)=\frac{1}{10}.P(C)=\frac{3}{5}\] \[P\left( \frac{E}{A} \right)=\frac{1}{4},P\left( \frac{E}{B} \right)=\frac{1}{3},P\left( \frac{E}{C} \right)=0\] \[\underset{p(he\,travelled\,by\,bus)}{\mathop{P\left( \frac{A}{E} \right)}}\,\] \[=\frac{P(A).P\left( \frac{E}{A} \right)}{P(A).P\left( \frac{E}{A} \right)+P(B).P\left( \frac{E}{C} \right)+P(C).P\left( \frac{E}{C} \right)}=\frac{9}{13}\]        


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