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JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    Three groups A, B, C are competing for positions on the Board of Directors of a company. The probabilities of their winning are 0.5, 0.3, 0.2 respectively. If the group A wins, the probability of introducing a new product is 0.7 and the corresponding probabilities for group B and C are 0.6 and 0.5 respectively. The probability that the new product will be introduced, is                                                [Roorkee 1994]

    A)                 0.18       

    B)                 0.35

    C)                 0.10       

    D)                 0.63

    Correct Answer: D

    Solution :

               Let \[E\] be the event that a new product is introduced.                    Then \[P(A)=0.5\], \[P(B)=0.3\], \[P(C)=0.2\]                    and \[P(E/A)=0.7,\,\,P(E/B)=0.6,\,\,P(E/C)=0.5.\]            \[\because \,\,\,A,\,\,B\] and \[C\] are mutually exclusive and exhaustive events.            \[P(E)=P(A)\,.\,P(E/A)+P(B)\,.\,P(E/B)+P(C)\,.\,P(E/C)\]            \[=0.5\times 0.7+0.3\times 0.6+0.2\times 0.5\]                 \[=0.35+0.18+0.10=0.63.\]


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