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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 16

  • question_answer
    A is one of 6 horses entered for a race, and is to be ridden by one of two jockeys B and C. It is 2 to 1 that B rides A, in which case all the horses are equally likely to win. If C rides A, his chances of winning is tripled. What are the odds against winning of A?

    A) 5 : 13           

    B) 5 : 18

    C) 13 : 5               

    D) none of these

    Correct Answer: C

    Solution :

    [c] : Let us define the events as \[{{E}_{1}}\]: Jockey B rides horse A \[{{E}_{2}}\]: Jockey C rides horse A \[E\]: The horse A wins \[\therefore \]\[P({{E}_{1}})=\frac{2}{3}\][Since odds in favour of \[{{E}_{1}}\]are 2:1] and \[P(E/{{E}_{1}})=\frac{1}{6}\] Again \[P({{E}_{2}})=1-P({{E}_{1}})=1-\frac{2}{3}=\frac{1}{3}\] and \[P(E/{{E}_{2}})=3P(E/{{E}_{1}})=\frac{1}{2}\] Now, the required probability == P(E) \[=P({{E}_{1}}\cap E)+P({{E}_{2}}\cap E)\] \[=P({{E}_{1}})P(E/{{E}_{1}})+P({{E}_{2}})P(E/{{E}_{2}})\] \[=\frac{2}{3}.\frac{1}{6}+\frac{1}{3}.\frac{1}{2}=\frac{5}{18}\] Therefore the odds against winning of A are 13:5.


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