What Is the Probability of Getting a Lift Within an Hour?

  • Thread starter nathangrand
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  • #1
nathangrand
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Cars pass at randoms times at an average rate of one a minute. The chance of a car stopping to give you a lift is one percent. What is the probability you will have got a lift within one hour?

This has pretty much stumped me. I know λ=60 as expecting 60 cars an hour for the poisson distribution but there's a binomial aspect to this as well because of each car either giving you a lift or not giving you a lift
 
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  • #2
It's probably easiest to calculate the probability you don't get a ride and then subtract that from 1.
 
  • #3
I agree! But how?
 
  • #4
What's the probability that exactly n cars pass in an hour?
 
  • #5
If N is the number of cars passing in time t, the event E = {no ride in time t} consists of {N=0} or {N=1 & no ride} or {N=2 & no ride} or ... . Are you familiar with the exponential series? If not, see http://en.wikipedia.org/wiki/Exponential_function .

RGV
 

FAQ: What Is the Probability of Getting a Lift Within an Hour?

What is Poisson Probability?

Poisson Probability is a mathematical concept used to calculate the probability of a certain number of events occurring within a specific time interval. It is named after French mathematician Siméon Denis Poisson and is often used to model rare events, such as the number of accidents in a given day or the number of customers arriving at a store in an hour.

How is Poisson Probability calculated?

To calculate Poisson Probability, you need to know the average rate of occurrence for the event, denoted by λ (lambda). The formula for calculating Poisson Probability is P(x) = (e^-λ * λ^x) / x!, where x is the number of events and e is the mathematical constant approximately equal to 2.71828.

What are the assumptions of Poisson Probability?

The assumptions of Poisson Probability include that the events occur independently of each other, the average rate of occurrence remains constant over time, and the probability of an event occurring is proportional to the length of the time interval. Additionally, the events must be rare, meaning that the probability of more than one event occurring at the same time is very small.

How is Poisson Probability used in real-world applications?

Poisson Probability is commonly used in fields such as finance, biology, and engineering to model rare events and make predictions. For example, it can be used to estimate the number of credit card fraud cases in a month, the number of mutations in a DNA sequence, or the number of machine failures in a manufacturing plant.

What is the difference between Poisson Probability and Binomial Probability?

While both Poisson Probability and Binomial Probability are used to calculate the probability of events, they differ in their assumptions and applications. Poisson Probability is used for rare events over a continuous time interval, while Binomial Probability is used for a fixed number of events over a discrete interval. Additionally, Poisson Probability assumes that the events occur independently, while Binomial Probability assumes a fixed probability of success for each event.

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