When I ride my bike from my house to my office, the trip is 8 miles long. Assume that I am equally likley to get a flat tire at any point on my ride. Let X denote the distance away from my office on my ride to work.

a) Draw the probability density function, f(x), for me getting a flat tire on my way to work at a distance x away from my office. Be sure to label the height of f(x).

b) What's the probability that a given flat tire happens within a half mile of my house?

c) What's the probability that a given flat tire happens within a half mile of my office?

d) Assume that if I get a flat I'll either walk back home or walk to my office. What's the probability that I'll have to walk more than 1 mile if I get a flat tire?