# Suppose that you get into a car accident at an average rate of about one accident every 3 years. In the next 21 years, you would expect to have about 7 accidents. if you actually had 5 accidents in that time, can you say that you're a better driver?

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Explain briefly using Poisson distribution or other methods.

Explain briefly using Poisson distribution or other methods.

##### 2 Answers

You could say so, but people some people are better drivers/have more experience, etc.

#### Explanation:

You could think of it like that, but for example a younger 18 year old is more likely to have crashes, more than a 39 year old. So therefore that person is bringing up the average crashes.

So maybe if for example you are 21, look at the average time for a crash between 18-22 year olds or similar, or you could do a questionnaire and compare yourself to others, then you can see if you are really a better driver.

Answer considering Poisson distribution...

#### Explanation:

This problem is heavily influenced by factors we simply dont know, like Brandon mentioned, a like age etc... but we can attempt to model this situation with a poisson distribution

We know Poisson:

In this case

So hence your rate,

Hence we can recal our properties about poisson distribution...

if

then

So hecne let

Now recal

So hecne our probability of getting in 7 accidents:

5 accidents

So actually the probability of being in 7 accidents over that time is relitivly small , so from this statement we can say that the driving is good, but not as much as first considered... But getting in 5, is even less likely in calculations...