Let a computer program generate only the digits 0 and 1 to form a string of binary numbers…

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 :

Accepted Answer

P(0 at even place) = $${1 \over 2}$$

P(0 at odd place) = $${1 \over 3}$$

P(1 at even place) = $${1 \over 2}$$

P(1 at odd place) = $${2 \over 3}$$

P(10 is followed by 01)

= $$\left( {{2 \over 3} \times {1 \over 2} \times {1 \over 3} \times {1 \over 2}} \right) + \left( {{1 \over 2} \times {1 \over 3} \times {1 \over 2} \times {2 \over 3}} \right)$$

= $${1 \over {18}} + {1 \over {18}}$$

= $${1 \over 9}$$

Solutions · 1