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 \(\frac{1}{2}\) 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, 17 Mar (Shift 2)]

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 \(\frac{1}{2}\) 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, 17 Mar (Shift 2)]

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