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 :
Correct Option: , 2
Solution:
$P($ second $A$ - card appears before the third $B$ - card)
$=P(A A)+P(A B A)+P(B A A)+P(A B B A)+P(B B A A)$
$+P(B A B A)$
$=\frac{1}{4}+\frac{1}{8}+\frac{1}{8}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{11}{16}$
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