A circular racetrack

sourabh33 wrote:A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?

A. 1/6
B. 2/6
C. 3/6
D. 1/12
E. 3/12

OA B

Total no. of sign posts on the circular=30; now out of these 30 sign posts any 1 sign post or the location from which car starts its journey can be selected in 30C1 ways;

in order to make a car stop within a half mile of the sign indicating 2 1/2 miles, we must start the journey of the car from any of the ( 0.6 mile to 1.5 mile sign posts ), which are total 10 in number,
(consider the following diagram to understand why its 10 in number);
(2----2.5----3)i.e. half mile can be on either side of the 2.5 mark ..!!

hence required probability is 10C1/30C1=10/30=1/3 hence B