Thousands of people are going to a Grateful dead concert in Pauley Pavillion 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?

Question

Jerimiah Kim

Mathematics

30 October, 12:59

Thousands of people are going to a Grateful dead concert in Pauley Pavillion 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?

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Rivera · Answer 1

2/3

Step-by-step explanation:

The expected length of a space is 1/2 * (10 ft) = 5 ft. So, the length of a car and a space is 10+5 = 15 feet. The car takes up 10 feet of that, or 10/15 = 2/3 of the total.

About 2/3 of the street will be covered with cars.