JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Probability

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In a box, there are 20 cards, out of which 10 are labeled 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. The probability that the second A - card appears before the third B - card is:

(A) $\frac{9}{16}$
(B) $\frac{15}{16}$
(C) $\frac{13}{16}$
(D) $\frac{11}{16}$ ✓ Correct

Answer: (D)

Solution

Each draw is A or B with probability

\frac{1}{2}

, independently. The second A arrives before the third B exactly in the sequences AA, ABA, BAA, ABBA, BBAA and BABA, with probabilities

\frac{1}{4}, \frac{1}{8}, \frac{1}{8}, \frac{1}{16}, \frac{1}{16}, \frac{1}{16}

. Adding them, the probability is

\frac{4 + 2 + 2 + 1 + 1 + 1}{16} = \frac{11}{16}

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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