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#1 2013-04-24 19:58:07

noemi
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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 (2013-04-24 20:29:44)

#2 2013-04-24 23:33:11

SteveB
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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.)

#3 2013-04-25 00:56:24

bobbym
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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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#4 2013-04-25 01:21:48

noemi
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Re: probability-easy one

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

#5 2013-04-25 01:46:03

bobbym
Administrator

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Re: probability-easy one

Wunderbar!


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#6 2013-04-25 02:09:36

bob bundy
Moderator

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Re: probability-easy one

hi noemi

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

Bob


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

#7 2013-04-25 04:10:56

noemi
Super Member

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Re: probability-easy one

it was my way too wink

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