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JEE Main & Advanced Mathematics Question Bank Critical Thinking

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    India plays two matches each with West Indies and Australia. In any match the probabilities of India getting point 0, 1 and 2 are 0.45, 0.05 and 0.50 respectively. Assuming that the outcomes are independents, the probability of India getting at least 7 points is [IIT 1992; Orissa JEE 2004]

    A)                 0.8750  

    B)                 0.0875

    C)                 0.0625  

    D)                 0.0250

    Correct Answer: B

    Solution :

               Matches played by India are four. Maximum points in any match are 2.            \[\therefore \] Maximum points in four matches can be 8 only.            Therefore probability \[(P)=p(7)+p(8)\]            \[p(7)={}^{4}{{C}_{1}}(0.05){{(0.5)}^{3}}=0.0250\]            \[p(8)={{(0.5)}^{4}}=0.0625\]                 \[\Rightarrow P=0.0875\].


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