simple maths task :>
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21 Oct 2010, 20:25
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Journals
plz who already knows the solution, dont write it :)
Task:
if there are 30 accidents in the month, what is the probability for having every day exactly 1 accident?
(ps: u can assume for every accident, its equiprobable, if an accident happens today or tomorrow)
ps: u can assume, month consists of 30 days
PS: plz write the solution way (explain the way), not the number, which i dont understand, how u got it
TIP: use COMBINATORICS
Since no one could solve it, i give an answer. Maybe someone gonna find out, how to get that probability:
1,2883161*10(to the power of -12)
Task:
if there are 30 accidents in the month, what is the probability for having every day exactly 1 accident?
(ps: u can assume for every accident, its equiprobable, if an accident happens today or tomorrow)
ps: u can assume, month consists of 30 days
PS: plz write the solution way (explain the way), not the number, which i dont understand, how u got it
TIP: use COMBINATORICS
Since no one could solve it, i give an answer. Maybe someone gonna find out, how to get that probability:
1,2883161*10(to the power of -12)
?
[edit]
30 accidents per month, 12 months in a year.
30x12=360.
Year has 365 days
360÷365=0,98630137
Am I even close?:P
[edit2]
Its not gonna work like this if you change the month to a one specific with 30 days, then the outcome would be exactly one.
edit: i suck at maths :(
p^30? Or?
-.-
If you've never done this math problem before, then go ahead.
whats the chance u have every day in a month 1 accident
possibilities: 30 first day none rest of the days
29 first day 1 second day none rest of the days
etc etc
if u know how much possiblilities there are its not hard to calculate whats the chance u have to get each day 1 accident
im 28 and i studied maths..? so im sure i know a lot about maths atleast more than you;)
in holland we are well educated and im a teacher maths now at the university of Utrecht
and btw, thx for the profile hit
I rofled while i wrote this : D
first day 1/30
second day 1/29
third day 1/28
and so on
On the last day its 1/1 so 100 % that an accident will happen ? :X
http://en.wikipedia.org/wiki/Poisson_distribution
really simple example of the poisson distribution that is
Your example is pretty simple since both lambda=1 and k=1
its 30 accidents in 30 days, we want to know it for ONE day so its 30/30 = 1
# lambda is a positive real number, equal to the expected number of occurrences that occur during the given interval.
the expected number in your case is one (one accident per day)
and i used the possion distribution because thats what you take to solve this :p
your period of time = 1 day, average rate = 30 per month => 1 per day (average)
actually, thinking about it, its probably not correct because this is the probability of it happening one time on one day (leaving the rest of the 29 days out of the equation)
I wont explain u this theory, because it is definately the wrong modell (very difficult, if possible) to solve that simple task. Btw, i wouldnt ask a task there to require the knowledge of that distribution. Everything is much easier
In that case: every day 1 accident:
(1/30!)
1/30 = 0.0333
quod erat demonstrandum
likelyhood calculations are easy
didnt know where you were going witht his but you can answer your question with a proper calculation if you actually intend to do so and this isnt thought to "troll" the people here.
And no, u dont need it there.
btw, this task is on the task sheet for complet beginners of the lecture on probability theory, and the school knowledge of stochastics is enough for solving the task
i said you can not make a proper probability calculation without knowing more parameters.
and i dont claim to be a statistics god. the complete opposite to be exact. my statistics book rots somewhere and i am not willing to calculate any more stats in my entire life. thats for accounting nerds and people tkaing their knowledge from learning books by heart.
1 thing i didnt said should be self-evident: the distribution of every individual accident is over all days uniform distributed, that means: if we take 1 accident, its equiprobable, if it happens today or tomorrow.
More things u dont need to know to find out the probability
and ofc you need to know like 30 acciedents but how many people?
if there is a sample size of 20 people having 30 accidents in 30 days its different from 1000000000 people having 30 accidents in 30 days.
I give u a tip: use COMBINATORICS, thats all u need :)
but ur not the first who asks for solution
so whats the point to tell it to everybody? :)
n <= 29
the probability for having 1 accident on day 1: P(1) = 1/30*29/30
day 2: P(2)= 1/29*28/29
day n: P(n) = 1/(31-n)*(30-n)/(31-n)
day 30: P(30) = 1
probability of all days together: P(1)*P(2)*...*P(n)
= 1/30*29/30*1/29*28/29*...*1/(31-n)*(30-n)/(31-n)
= 1/30*1/29*...*1/2 * 29/30*28/29*27/28*...*3/4*2/3*1/2
= 1/30! * 1/30
= 1.25 * 10^-34
nice to see u there too :)
"the probability for having 1 accident on day 1: P(1) = 1/30*29/30"
thats already wrong.
The statement: "the probability for having 1 accident on DAY 1" should be expressed in the following way:
1/30 * (29/30)^29 * 30
that means: 1/30 that 1st accident is on the 1st day, (29/30)^29 for the rest 29 accidents beeing on other days and "*30" because every accident can be on the 1st day.
Ur expression " P(1) = 1/30*29/30"" would only mean, that the 1st accident is on the 1st day, and the 2nd accident is not on the 1st day.
ps: there is a shorter way. Just try to count the number of interesting results and devide by the amount of all results. Its very short and simple term :)
All results: 30^30
yeah I guess I couldn't just concentrate before when my gf is making strange sounds :$
hey btw :p
btw, why do u always ask probabilistics, we want rather some cases where we have to form differentials or something more interesting, I hate statistics and probs :D
is it because of the strange movements? ;)
anyway, I guess you couldn't concentrate either if somebody is eating watermelon and pineapple next to you and listening to lady gaga :O
Anyway, I've had a large course on stats and probs but I just don't like them at all :l
but surely I'm up to those tasks as well, like u said mostly combitorials are possible to think through without any deeper knowledge
why dont u like statistics? It is such a great think, for example to estimate unknown parameters using interesting methods :)
Here a simple statistical task: how to estimate in a simplest way, how many fishes ar in the small sea?
And well statistics I just don't consider that interesting, I like rather solving some interesting problems where you have to think it through in your head rather than study some ready curves that you can apply in the exes :) (And yeah, I know statistics is a lot more than that, but I just hate studying stuff :D)
Well, I haven't ever really studied an exe like this or at least can't remember, but I guess I would count the amount of fishes in some small area and then just suppose that the fish density is the same throughout all the sea :P
to count an amount in a special area would be not right, because fishes might be swimming in groups in specific places and ar moving. What could be another much better solution?
You have to know something about fishes' style of living and suppose that they tend to live in groups or have some insight if they like to live rather in the deeper parts or closer to surface etc :)
I guess my example would work in a static situation where the fishes would be scattered all around randomly.
But about this case, I don't know why but I'd like to apply quantum mechanics and take the probabilities that way generalized for many particles but guess u don't like that method much :D
you can tell me yours :)
mark a big amount of fishes and let them swim and mix up over all the fishes in the sea. After a period of time make a sample by catching some amount and compare the proportion of fishes u marked to all fishes. U can do some samples to improve the estimation, and build the mean :)
so how u like it? :D
But what is long enough time for them to scatter around especially if you only let them out at one special place :D ? And how did u catch them in the first place for marking? Maybe those fishes prefer some certain areas of the sea :D Well I think your model works mathmetically fine if you tell me the time table and otherwise we will face all the real life factors that prevent the world from working ideally :P
Let's say that I like the probabilistics more and looking forward to your next question :D ?
1. U can mark young fishes, which grew up in special pools, and let them after into the sea.
2. Let them mix up enough time (zoologist know it better)
any math task for tonight !?
4 what the math
1 devided by 30 by the power of 30 making it
4.86 x 10 ^ -43 percent that you have exactly 1 accident each day