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

Step-by-step solution

Given the probability that the digit 0 appear at the even place is 1 2 , hence the probability that the digit 1 appear at the even place is 1 - 1 2 = 1 2 . And the probability that the digit 0 appear at the odd place is 1 3 , hence the probability that the digit 1 appear at the odd place is 1 - 1 3 = 2 3 . For the digits ' 10 ' and ' 01 ' we have the following possibilities 1 0 0 1 o d d   p l a c e e v e n   p l a c e o d d   p l a c e e v e n   p l a c e Or 1 0 0 1 e v e n &#16