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KVPY Sample Paper KVPY Stream-SX Model Paper-11

  • question_answer
    An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is:

    A) \[\frac{26}{49}\]           

    B) \[\frac{32}{49}\]

    C) \[\frac{27}{49}\]           

    D) \[\frac{21}{49}\]

    Correct Answer: B

    Solution :

    \[{{E}_{1}}\] : Event of drawing a red ball and placing a green ball in the bag
    \[{{E}_{2}}\] : Event of drawing a green ball and placing a red ball in the bag
    E : Event of drawing a red ball in second draw
    \[P(E)=P({{E}_{1}})\times P\left( \frac{E}{{{E}_{1}}} \right)+P({{E}_{2}})\times P\left( \frac{E}{{{E}_{2}}} \right)\]\[=\frac{5}{7}\times \frac{4}{7}+\frac{2}{7}\times \frac{6}{7}=\frac{32}{49}.\]


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