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JEE Math Practice Question

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 $${1 \over 2}$$ and probability of occurrence of 0 at the odd place be $${1 \over 3}$$. Then the probability that '10' is followed by '01' is equal to :

  1. A.$${1 \over 18}$$
  2. B.$${1 \over 3}$$
  3. C.$${1 \over 9}$$
  4. D.$${1 \over 6}$$

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