Let a computer program generate only the digits 0 and 1 to form a s...

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Let a computer program generate only the digits 0 and 1 to form a string of binary numbers with probability of
P occurrence of 0 at even places be \( \frac{1}{2} \) and probability of occurrence of 0 at the odd place be \( \frac{1}{3} \). Then the probability that ' 10 ' is followed by' 01 ' is equal to:
[JEE Main-2021 (March)]
(a) \( \frac{1}{18} \)
(b) \( \frac{1}{3} \)
(c) \( \frac{1}{9} \)
(d) \( \frac{1}{c} \)
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