Question

Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D?

• A. $\frac{8}{13}$
• B. $\frac{13}{64}$
• C. $\frac{119}{128}$
• D. $\frac{9}{128}$

Answer 1

The correct option is D $\frac{9}{128}$


Let X = {waiting time at B}, Y = {waiting time at C},
Manish will arrive late only when $13<x+y\le 16$

$P(x+y>13)=\frac{ShadedArea}{TotalArea}=\frac{\frac{1}{2}\times 3\times 3}{8\times 8}=\frac{9}{128}$