JEE Main & Advanced Mathematics Question Bank Critical Thinking

  • question_answer
    An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding the numbers on the two faces is noted. If the result is a tail, a card from a well shuffled pack of eleven cards numbered 2, 3, 4,.......,12 is picked and the number on the card is noted. The probability that the noted number is either 7 or 8, is [IIT 1994]

    A)                 0.24       

    B)                 0.244     

    C)                 0.024     

    D)                 None of these

    Correct Answer: B

    Solution :

               Required probability = probability that either the number is 7 or the number is 8.                    i.e., Required  Probability \[={{P}_{7}}+{{P}_{8}}\]            Now \[{{P}_{7}}=\frac{1}{2}.\frac{1}{11}+\frac{1}{2}.\frac{6}{36}=\frac{1}{2}\left( \frac{1}{11}+\frac{1}{6} \right)\]            \[{{P}_{8}}=\frac{1}{2}.\frac{1}{11}+\frac{1}{2}.\frac{5}{36}=\frac{1}{2}\left( \frac{1}{11}+\frac{5}{36} \right)\]                 \[\therefore \,\,\,P=\frac{1}{2}\left( \frac{2}{11}+\frac{11}{36} \right)=0.244.\]


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