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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 class of 125 students 70 passed in Mathematics, 55 in Statistics and 30 in both. The probability that a student selected at random from the class has passed in only one subject is                                        [EAMCET 1993]

    A)                 \[\frac{13}{25}\]  

    B)                 \[\frac{3}{25}\]

    C)                 \[\frac{17}{25}\]  

    D)                 \[\frac{8}{25}\]

    Correct Answer: A

    Solution :

                       Consider the following events :                    \[A=\] A student is passed in Mathematics,                    \[B=\] A student is passed in Statistics.                    Then \[P(A)=\frac{70}{125},\] \[P(B)=\frac{55}{125},\] \[P(A\cap B)=\frac{30}{125}.\]                    Required probability is                    \[P(A\cap \bar{B})+P(\bar{A}\cap B)\]\[=P(A)+P(B)-2P(A\cap B)\]                                 \[=\frac{70}{125}+\frac{55}{125}-\frac{60}{125}=\frac{65}{125}=\frac{13}{25}.\]


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