JEE MainMathematicsEasyProbability

In an box, there are 20 cards, out of which 10 are labelled as A
and the remaining 10 are labelled as B. Cards are drawn at random, one
after the other and with replacement, till a second A-card is obtained.
Then find the probability that the second A-card appears before the
third B-card

Show answer and solution

AA + ABA + BAA + ABBA + BBAA + BABA

= \frac{1}{4} + \frac{1}{8} + \frac{1}{8} + \frac{1}{16} + \frac{1}{16} + \frac{1}{16} = \frac{11}{16}

Source: Grass-G / M-08 Mathematics Paper 23 October.docx

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