Verified Solution • 2025–26 Session moderate

QJEEM20Maf55a: JEE Main 2020 Mathematics - Class 12 JEEM20Maf55a Solution: In a box, there are 20 cards, out of which 10 are lebelled as A …

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 :

Multiple Choice Options

  • A 1316{{13} \over {16}}
  • B 1116{{11} \over {16}}
  • C 1516{{15} \over {16}}
  • D 916{{9} \over {16}}

Step-by-Step Verified Solution

Possibilities that the second A card appears before the third B card are
=AA + ABA + BAA + ABBA + BBAA + BABA

= (12)2{\left( {{1 \over 2}} \right)^2} + (12)3{\left( {{1 \over 2}} \right)^3} + (12)3{\left( {{1 \over 2}} \right)^3} + (12)4{\left( {{1 \over 2}} \right)^4} + (12)4{\left( {{1 \over 2}} \right)^4} + (12)4{\left( {{1 \over 2}} \right)^4}

= 14{1 \over 4} + 18{1 \over 8} + 18{1 \over 8} + 116{1 \over {16}} + 116{1 \over {16}} + 116{1 \over {16}}

= 1116{{11} \over {16}}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring