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Topic: some confusing math probablity problems
Replies: 3   Last Post: Apr 10, 2014 11:06 PM

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Stan Brown

Posts: 1,320
Registered: 12/6/04
Re: some confusing math probablity problems
Posted: Apr 10, 2014 6:21 AM
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On Wed, 09 Apr 2014 22:13:33 -0500, stony wrote:
>
>
> P1. A bus comes to a station once every 10 minutes and waits at the
> station for 1.5 minutes.


The problem says "a bus comes every 10 minutes", not "a bus comes 10
minutes after the previous one leaves".

> question 1. Find the probability that the bus will be at te station
> when you arrive (Book answer: 0.15) - (our answer 0.13 - 1.5/11.5)
> ours is wrong


"Without loss of generality", as they say, assume that the buses
arrive on the hour and at 10, 20, 30, 40, and 50 minutes past the
hour. They then leave at 1.5, 11.5, 21.5, 31.5, 41.5, and 51.5
minutes past the hour.

During what proportion of the time is there a bus in the station?
During what proportion of any ten-minute period is there a bus in the
station?

> question 2. IF you go to the station 20 times, predict about how many
> times you will have to wait less than 3 minutes. (book answer: 9
> times) - (our answer which is wrong is: (3/11.5) * 20 = 7.xxx)


Aside from the error I mentioned above, your numerator "3" assumes
that if a bus is already standing in the station you must
nevertheless wait for it.

What proportion of any ten-minute period is within the 3 minutes
before the arrival of a bus, or the 1.5 minutes while it is standing
there?

> P2. A radio station gives a weather report every 15 minutes. Each
> report lasts 45 seconds. Suppose you turn on the radio at a random
> time.


I won't solve these because you didn't say what you got, but I
suspect you made the same error. The problem does not say that each
report starts 15 minutes after the end of the previous one.

> Question 1. Find the probability that you will have to wait more than
> 5 minutes to hear the weather report
>
> Question 2. If you turn on the radio at 50 random times, predict about
> how many times you will hahve to wait less than 1 minute before the
> start of the next weather report.
>
>
> I don't understand how it works obviously. We did other geometric
> prob problems, but these two are confusing. Please explain your
> answers. I am a little confused myself. thanks


I don't understand why you call these "geometric probability". There
is no geometry here that I can see.


--
Stan Brown, Oak Road Systems, Tompkins County, New York, USA
http://OakRoadSystems.com
Shikata ga nai...



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