KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    A pair of unbiased dice is rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is

    A) \[2/5\]   

    B) \[3/5\]

    C) \[4/5\]               

    D) \[\frac{1}{5}\]

    Correct Answer: A

    Solution :

    Consider the events
    A = Sum of 5 occurs
    B = Sum of 7 occurs
    C = Neither sum of 5 nor sum of 7 occurs
    P (A occurs before B) \[=P(A\,\text{or}\,(C\cap A)\,\text{or}\,(C\cap C\cap A)\,\text{or}...)\]
    \[=\frac{1}{9}+\frac{13}{18}\times \frac{1}{9}+{{\left( \frac{13}{18} \right)}^{2}}\times \frac{1}{9}+...\]
    \[=\frac{1}{9}\left( 1+\frac{13}{18}+{{\left( \frac{13}{18} \right)}^{2}}+... \right)\]
    \[=\frac{1}{9}\left( \frac{1}{1-\left( \frac{13}{18} \right)} \right)=\frac{2}{5}\]

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