Probability of Taxi Arrival in 10 Minutes After 1 Hour Wait

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The discussion revolves around calculating the probability of a taxi arriving within 10 minutes after waiting for one hour, given that the time between taxi arrivals is exponentially distributed with a mean of 10 minutes. The user initially attempted to set up the integral but struggled with the limits, mistakenly thinking subtraction was necessary. Clarification was provided that this is a conditional probability problem, requiring the calculation of Pr(60 < t < 70) given Pr(60 < t). The correct approach involves using the formula for conditional probability to find the intersection of events. Ultimately, the user seeks guidance on properly setting up the limits for their integral to arrive at the correct probability.
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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 can't 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.
 
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mikemike123 said:
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 can't 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.

Not subtract. You have a conditional probability here.
 
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)?
 
mikemike123 said:
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)?

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

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