In a box, there are 20 cards,
Question:

In a box, there are 20 cards, out of which 10 are labelled as $\mathrm{A}$ and the remaining 10 are labelled as $\mathrm{B}$. 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 :

1. (1) $\frac{9}{16}$

2. (2) $\frac{11}{16}$

3. (3) $\frac{13}{16}$

4. (4) $\frac{15}{16}$

Correct Option: , 2

Solution:

$P($ second $A$ – card appears before the third $B$ – card)

$=P(A A)+P(A B A)+P(B A A)+P(A B B A)+P(B B A A)$

$+P(B A B A)$

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