Question

Thousands of people are going to a Grateful dead concert in Pauley Pavillion at UCLA. They park their the foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on .0; 10/. In the long run, what fraction of the street is covered with cars

Answer 1

This question is incomplete, the complete question is;

Thousands of people are going to a Grateful dead concert in Pauley Pavilion at UCLA. They park their 10 foot cars on several of the long streets near the arena. There are no lines to tell the drivers where to park, so they park at random locations, and end up leaving spacings between the cars that are independent and uniform on ( 0, 10 ). In the long run, what fraction of the street is covered with cars?.

Answer:

in the long run, the fraction of street that will be covered with cars is 0.6667

Step-by-step explanation:

 given the data in the question;

the gaps between two cars follows uniformly ) 0, 10 )

therefore in the long run, average gap will be;

⇒ (0 + 10) / 2 = 10 / 2 = 5 feet

meaning that, in the long run a single car will occupy;

⇒ length of car + gap

⇒ 10 + 5 = 15 feet

∴ the fraction of road covered with cars will be;

⇒ length of car / space or length of road occupied by one car

⇒ 10 / 15

⇒ 0.6667

Therefore, in the long run, the fraction of street that will be covered with cars is 0.6667