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So I just took a probability test and I'm having a hard time with the fact that my answer is wrong. I've done some research online and I believe I am correct, I was hoping to get some input. I'm new to using LaTeX so sorry if it's sloppy. Thanks!

Problem: Suppose that the amount of time in minutes that I wait for a bus is uniformly distributed on the interval [0,60].

2. Relevant equations

3. The attempt at a solution

(I got part A correct)

Part A: What is the probability I have to wait for at least 20 minutes?

Solution:

[tex]P(X \geq 20 ) = 1 - P(X \leq 20) = 1 - \int_0^{20} \frac{1}{60} dx = 1 - \frac{20}{60} = 1 - \frac{1}{3} = \frac{2}{3}[/tex]

(I got part B wrong)

Part B: Suppose that when I arrive at the bus stop, I meet someone else who has already been waiting for the same bus for 20 minutes. If I take that information into account, what is the probability that I will have to wait for at least 20 minutes?

Solution:

[tex]P(X \geq 20 ) = 1 - P(X \leq 20) = 1 - \int_0^{20} \frac{1}{40} dx = 1 - \frac{20}{40} = 1 - \frac{1}{2} = \frac{1}{2}[/tex]

Since someone else has already been waiting for the same bus for 20 minutes and has not been picked up yet, I would think we could change the sample space? So I used an interval of length 40, since the original was 60.

P.S. I used this site:

http://cnx.org/content/m16819/latest/

Example 2, Problem 3.

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# Homework Help: Uniform Distribution with Conditional Probability

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