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JEE Main 2021 · Mathematics · Probability · hard

Urn I has 3 red and 2 blue balls; urn II has 2 red and 4 blue balls. An urn is chosen at random and one ball is drawn, which turns out to be red. The…

Single correct option

Urn I has 33 red and 22 blue balls; urn II has 22 red and 44 blue balls. An urn is chosen at random and one ball is drawn, which turns out to be red. The probability that it came from urn I is
  1. A. 514\dfrac{5}{14}
  2. B. 35\dfrac{3}{5}
  3. C. 928\dfrac{9}{28}
  4. D. 914\dfrac{9}{14}
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Answer: (D) 914\dfrac{9}{14}

By Bayes' theorem, P(I∣R)=12⋅3512⋅35+12⋅13=3/53/5+1/3=9/1514/15=914P(\text{I}\mid R)=\dfrac{\tfrac12\cdot\tfrac35}{\tfrac12\cdot\tfrac35+\tfrac12\cdot\tfrac13}=\dfrac{3/5}{3/5+1/3}=\dfrac{9/15}{14/15}=\dfrac{9}{14}. The option 35\tfrac35 ignores the other urn's contribution to the denominator.
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Original question written in the JEE Main 2021 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake