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#1 2013-04-23 21:58:07

noemi
Member
Registered: 2010-01-07
Posts: 2,333

probability-easy one

Hey.. many years have gone by since I've done this exercises..so I need to check some answers..
2 number cubes are rolled. a)What is the probability of getting 6 at least on one cube?  b)What is the probability of getting a number 6 if we know that the sum of two numbers is 8?

Last edited by noemi (2013-04-23 22:29:44)

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#2 2013-04-24 01:33:11

SteveB
Member
Registered: 2013-03-07
Posts: 557

Re: probability-easy one

(a) 11/36
(b) 2/5

I am absolutely sure about the first one, but have a slight nagging doubt about the second.
The thing that occurs to me is Bayes Theorem, and I haven't studied that for a long time.
I therefore decided to think about how many possible combinations added to 8:

6,2
5,3
4,4
3,5
2,6

Then noticed that two of them contained a six. So (2/5)

The thing that made me think of Bayes was that it was "something given something else", but I cannot think how
Bayes could be used in this example. Perhaps it is ((2/36)/(5/36))
Bayes formula would be:  P(K|C) = P(KC)/P(C)
So would it be valid to let  P(KC) be the chance of getting an 8 which also contains a six ?
With P(C) as the chance of getting a total of 8.
With P(K) as the chance of the role containing a six.
With P(K|C) as the chance of the role containing a six given that the total is 8.

(Someone needs to check all of that because I am not sure of it. Haven't done this for ages.)

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#3 2013-04-24 02:56:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: probability-easy one

Hi;

a)

Using a gf:

P(at least 1 six) = 1 - 25 / 36 = 11 / 36

b) Enumeration is fine but for a gf, here is one.

The ways to make an 8 are 2sx^2 and 3x^8. So the answer is 2 / 5.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#4 2013-04-24 03:21:48

noemi
Member
Registered: 2010-01-07
Posts: 2,333

Re: probability-easy one

great.. I got the same results!
Tnx..

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#5 2013-04-24 03:46:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 87,258

Re: probability-easy one

Wunderbar!


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#6 2013-04-24 04:09:36

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,427

Re: probability-easy one

hi noemi

Well done for getting the answers.  Too late but here's my way. See diagram.

Bob

View Image: noemi.gif

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2013-04-24 06:10:56

noemi
Member
Registered: 2010-01-07
Posts: 2,333

Re: probability-easy one

it was my way too wink

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