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Question

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


A

16

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B

118

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C

19

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D

13

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Solution

The correct option is C

19


Explanation for the correct answer:

Finding the probability that '10' is followed by '01':

Given,

P(0atevenplaces)=12P(0atoddplaces)=13P(1atevenplaces)=1-12=12P(1atoddplaces)=1-13=23

There are only two possibilities to arrange 0110

Possibility 1: Odd Even Odd Even

Possibility 2: Even Odd Even Odd

P ('10' is followed by '01')

=13*12*23*12+12*23*12*13=118+118=19

Hence, option (C) is the correct answer.


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