R help - Feb 2011 - Calculate probabilty

Hi List,

I have a question to calculate probability using R.

There are 491 boxes and 142 balles. If the ball randomly put into the
box. How to calculate the probability of six or more there are in one
box?

I have try :

dbinom(6,142,1/491)

1-pbinom(6,142,1/491)

But I think I have some unclear about the dbinom and pbinom.

Thank you very much in advance.

Are you clear about the question you are asking?  Do you want to know whether
there are 6 balls or at least 6 balls?  (It sounds like "at least".) 
Do you want to know whether there are at least 6 balls in the first box, or at
least 6 balls in exactly one box or at least 6 balls in at least one box?

This is the probability that there are exactly 6 balls in the first
box:
> dbinom(6,142,1/491)
[1] 5.53366e-07
>
This is the probability that there are MORE THAN 6 balls in the first box:  (NOT
"at least 6")
> 1-pbinom(6,142,1/491)
[1] 2.272026e-08
> sum(sapply(7:142, function(i) dbinom(i,142,1/491)))
[1] 2.272026e-08
> 1-sum(sapply(0:6, function(i) dbinom(i,142,1/491)))
[1] 2.272026e-08

This is probability that there are at least 6 balls in the first
box:
> 1-pbinom(5,142,1/491)
[1] 5.760862e-07

You can get all this from ?dbinom, but it pretty confusing that the argument n
and the italic n in the details are totally different things, italic n =
argument size.  (Likewise, italic p = argument prob, not argument p.)

Questions about more than one box are a little harder since the boxes are not
independent.

HTH,
Rex

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Fabrice Tourre
Sent: Thursday, February 24, 2011 3:51 PM
To: r-help at r-project.org
Subject: [R] Calculate probabilty

Hi List,

I have a question to calculate probability using R.

There are 491 boxes and 142 balles. If the ball randomly put into the
box. How to calculate the probability of six or more there are in one
box?

I have try :

dbinom(6,142,1/491)

1-pbinom(6,142,1/491)

But I think I have some unclear about the dbinom and pbinom.

Thank you very much in advance.

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Hi Rex,

Thanks for you explain. In fact, my question is: When I observed that
there are 6 or more balls in one box, what is this probability? The
ball is randomly put into the boxes.
I think it is: 1-pbinom(6,142,1/491) = 2.272026e-08.

When the sample size is large, how should I do this? using chisq.test?
Becuase binom test is not suitable for large sample size.
For example,
There are 6000 balls and 500 boxes, when I observed that there are 60
or more balls in one box, what is this probability?

On Fri, Feb 25, 2011 at 6:40 PM,  <rex.dwyer at syngenta.com>
wrote:
> Rex