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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    Rahul has to write a project, probability that he will get a project copy is ?P?, probability that he will get a blue pen is ?q? and probability that he will get a black pen is 1/2, if he can complete the project either with blue or with black pen or with both and probability that he completed the project is 1/2 then \[P(1+q)\]is 

    A) \[\frac{1}{2}\]

    B) 1

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

    D) 2

    Correct Answer: B

    Solution :

    [c] Lets define the events as probability of getting project copy [a] = p Probability of getting blue pen [b] = q 0Probability of getting black pen [c] = 1/2 Then \[P(AC\overline{B})+p(AC\overline{B})+p(ABC)=\frac{1}{2}\] \[p.q.\frac{1}{2}+p.\frac{1}{2}(1-q)+p.q.\frac{1}{2}=\frac{1}{2}\] \[\therefore pq+p-pq+pq=1\]       \[\therefore p(1+q)=1\]


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