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JEE Main & Advanced JEE Main Paper Phase-I (Held on 08-1-2020 Evening)

  • question_answer
    Let A and B be two events such that the probability that exactly one of them occurs is \[\frac{2}{5}\]and the probability that A or B occurs is \[\frac{1}{2}\] , then the probability of both of them occur together is [JEE MAIN Held on 08-01-2020 Evening]

    A) 0.01                 

    B) 0.20

    C) 0.02                 

    D) 0.10

    Correct Answer: D

    Solution :

    Given \[P\left( A\cap \overline{B} \right)+P\left( \overline{A}\cap B \right)=\frac{2}{5}\] \[\Rightarrow \,\,\,\,\,\,\,P\left( A \right)+P\left( B \right)-2P\left( A\cap B \right)=\frac{2}{5}\] \[\Rightarrow \,\,\,\,\,P\left( A\cup B \right)-P\left( A\cap B \right)=\frac{2}{5}\] \[\Rightarrow \,\,\,\,\,\,\frac{1}{2}-\frac{2}{5}=P\left( A\cap B \right)\] \[\Rightarrow \,\,\,\,\,\,P\left( A\cap B \right)=\frac{1}{10}\]


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