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

  • question_answer
    A student appears for tests I, II and III. The student is successful if he passes either in tests I and II or tests I and IV. The probabilities of the student passing in tests I, II, III are p, q and \[\frac{1}{2}\] respectively. The probability that the student is successful is \[\frac{1}{2}\] then the relation between p and q is given by

    A) \[pq+p=1\]

    B) \[{{p}^{2}}+q=1\]

    C) \[pq-1=p\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Let A, B and C be the events that the student is successful in tests, I, II and III respectively. Then P(The student is successful) \[=P(A)P(B)\{1-P(C)\}+P(A)\{1-P(B)\}P(C)+\]\[P(A)P(B)P(C)\] \[=p.q\left( 1-\frac{1}{2} \right)+p(1-q)\frac{1}{2}+p.q\frac{1}{2}\] \[=\frac{1}{2}pq+\frac{1}{2}p(1-q)+\frac{1}{2}pq\] \[=\frac{1}{2}(pq+p-pq+pq)=\frac{1}{2}(pq+p)\] \[\therefore \frac{1}{2}=\frac{1}{2}(pq+p)\Rightarrow 1=pq+p\]


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