# Probability densities

1. ### mikemike123

5
Heres the question.... The time between arrivals of taxis at a busy intersection is exponentially distributed with a mean of 10 minutes.

The question I am stuck on is....

Suppose you have already been waiting for one hour for a taxi, what is the probability that one arrives within the next 10 minutes. (The first part of the problem was to find probability you wait longer then an hour which I figured the limits would be (60<x<infinity).

Well i know mew=beta=10 min=1/lambda=1/10

f(x)= lambda*e^-lambda which will ultimately give me 1/10e^-1/10xdx. I have my integral set up, the thing is I cant figure out my limits. My initial guess was to evaluate the integral from (0<x<60) and subtract (70<x<infinity), ultimately giving me the answer .9984 or 99.84%. I thought it was right but apparently wrong, can someone please help me set up the appropriate limits. Thanks in advance.

2. ### sylas

1,745
Not subtract. You have a conditional probability here.

3. ### mikemike123

5
Ok so if my given is the answer I got for my first part, .0025. How would I go on finding the Probability of P(AintersectB)?

4. ### sylas

1,745
You need Pr(60 < t < 70) given Pr(60 < t). What's the formula for that?