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

  • question_answer
    If an integer is chosen at random from first 100 positive integers, then the probability that the chosen number is a multiple of 4 or 6, is

    A)                 \[\frac{41}{100}\]

    B)                 \[\frac{33}{100}\]

    C)                 \[\frac{1}{10}\]    

    D)                 None of these

    Correct Answer: B

    Solution :

                       Let \[A\] be the event to be multiple of 4 and \[B\] be the event to be multiple of 6                    So, \[P(A)=\frac{25}{100},\] \[P(B)=\frac{16}{100}\] and \[P(A\cap B)=\frac{8}{100}\]                    Thus required probability is                    \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\]                                 \[\Rightarrow P(A\cup B)=\frac{25}{100}+\frac{16}{100}-\frac{8}{100}=\frac{33}{100}\].


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