In a box, there are 20 cards, out of which 10 are lebelled 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 :
Solution
Possibilities that the second A card appears before the third B card are
<br>=AA + ABA + BAA + ABBA + BBAA + BABA
<br><br>= ${\left( {{1 \over 2}} \right)^2}$ + ${\left( {{1 \over 2}} \right)^3}$ + ${\left( {{1 \over 2}} \right)^3}$ + ${\left( {{1 \over 2}} \right)^4}$ + ${\left( {{1 \over 2}} \right)^4}$ + ${\left( {{1 \over 2}} \right)^4}$
<br><br>= ${1 \over 4}$ + ${1 \over 8}$ + ${1 \over 8}$ + ${1 \over {16}}$ + ${1 \over {16}}$ + ${1 \over {16}}$
<br><br>= ${{11} \over {16}}$
About this question
Subject: Mathematics · Chapter: Probability · Topic: Classical and Axiomatic Probability
This question is part of PrepWiser's free JEE Main question bank. 143 more solved questions on Probability are available — start with the harder ones if your accuracy is >70%.