Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

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

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)*

Offline

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

(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.)

Offline

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

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.**

Offline

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

great.. I got the same results!

Tnx..

Offline

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

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.**

Offline

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

hi noemi

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

Bob

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

Offline

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

it was my way too

Offline

Pages: **1**