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JEE Main & Advanced Mathematics Probability Question Bank Odds in favour and odds against Addition theorem on probability

  • question_answer
    In a horse race the odds in favour of three horses are \[1:2\], \[1:3\] and \[1:4\]. The probability that one of the horse will win the race is

    A)                                                                                           \[\frac{37}{60}\]                                                                                        

    B)                                                                                           \[\frac{47}{60}\]

    C)                                                                                             \[\frac{1}{4}\]                                                                                           

    D)                                                                                             \[\frac{3}{4}\]

    Correct Answer: B

    Solution :

                       Probabilities of winning the race by three horses are                                                                                 \[\frac{1}{3},\,\,\frac{1}{4}\]  and                                                                                            \[\frac{1}{5}.\]                                                    Hence required probability                                                      \[=\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}.\]


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