Question

The adjoining figure is a map of part of a city: the small rectangles are blocks and the spaces in between streets. Each morning a student walks from intersection A to intersection B, always walking along streets shown, always going east or south. For variety, at each intersection where he has a choice, he choose with probability 1/2 (independent of all other choices) whether to go east or south. Find the probability that, on any given morning, he walks through intersection C.

• A. $\frac{11}{23}$
• B. $\frac{1}{2}$
• C. $\frac{4}{7}$
• D. None of these

Answer 1

The correct option is D None of these

Probability of the student walking through East or south $=\frac{1}{2}.$

If the boy passes through intersection $C,$ then he would choose a path east of the town and walk towards west So, as he walk South he would be passing through intersection $C$ to in reach intersection $D.$

$\therefore$ Probability of the choosing the odd on $7.$

$\Rightarrow$ Days of a work $=\frac{1}{7}\times \frac{1}{2}=\frac{1}{14}.$

Hence, the answer is none of these.