Verified Solution • 2025–26 Session moderate

QJEEM21Mad7c8: JEE Main 2021 Mathematics - Class 12 JEEM21Mad7c8 Solution: Let a computer program generate only the digits 0 and 1 to form …

Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of occurrence of 0 at even places be 12{1 \over 2} and probability of occurrence of 0 at the odd place be 13{1 \over 3} . Then the probability that '10' is followed by '01' is equal to :

Multiple Choice Options

  • A 118{1 \over 18}
  • B 13{1 \over 3}
  • C 19{1 \over 9}
  • D 16{1 \over 6}

Step-by-Step Verified Solution

P(0 at even place) = 12{1 \over 2}

P(0 at odd place) = 13{1 \over 3}

P(1 at even place) = 12{1 \over 2}

P(1 at odd place) = 23{2 \over 3}

P(10 is followed by 01)

= (23×12×13×12)+(12×13×12×23)\left( {{2 \over 3} \times {1 \over 2} \times {1 \over 3} \times {1 \over 2}} \right) + \left( {{1 \over 2} \times {1 \over 3} \times {1 \over 2} \times {2 \over 3}} \right)

= 118+118{1 \over {18}} + {1 \over {18}}

= 19{1 \over 9}

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