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JEE Main 20209 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2020 · 9 January · Morning Shift · Mathematics · Probability

In a box, there are 20 cards, out of which 10 are labelled as A and...

In a box, there are 2020 cards, out of which 1010 are labelled as AA and the remaining 1010 are labelled as BB . Cards are drawn at random, one after the other and with replacement, till a second AA card is obtained. The probability that the second AA card appears before the third BB card is:

Options

  1. A916\dfrac{9}{16}
  2. B1116\dfrac{11}{16}
  3. C1316\dfrac{13}{16}
  4. D1516\dfrac{15}{16}

Correct answer

B. 1116\dfrac{11}{16}

Step-by-step solution

P(A)=12P(B)=12P\left(A\right) = \dfrac{1}{2}P\left(B\right) = \dfrac{1}{2}

P(AA+ABA+BBA+ABBA+BBAA+BABA)=14+18+18+116+116+116=1116P\left(AA + ABA + BBA + ABBA + BBAA + BABA\right) = \dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{8} + \dfrac{1}{16} + \dfrac{1}{16} + \dfrac{1}{16} = \dfrac{11}{16}

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