Math Problem! Help Appreciated (:

[Dunzo]

Hey guys! I have a problem of the week for my math class I haven't really looked at it but if you all could help it would be greatly appreciated! If you agree with one person's answer please post saying so. Thanks!

Fibonacci Dice:

A fair die has faces bearing the numerals 1, 1, 2, 3, 5, and 8 - the beginning of the Fibonacci sequence. The die is rolled twice. What is the probabilty that the sum of the two rolls is a Fibonacci number?

[Hyzek]

7/18? adasdasdsa

[Dunzo]

i need the work and the answer as well! hopefully you guys can help out quickly enough (:

[HavokD]

Since Im a geek, I will offer you a full explanation, but this is a pretty simple exercise, I hope you understand it well so you can solve even more complex problems:

First of all, I would encourage you to write all the different results we would have by doing both throws. In short, our Space

(S)= {x , y| x,y € (1, 1, 2, 3, 5, 8)}

Where x is the result on the first throw, and y is the result on the second throw.

Or better yet:

1,1 1,1 1,2 1,3 1,5 1,8
1,1 1,1 1,2 1,3 1,5 1,8
2,1 2,1 2,2 2,3 2,5 2,8
3,1 3,1 3,2 3,3 3,5 3,8
5,1 5,1 5,2 5,3 5,5 5,8
8,1 8,1 8,2 8,3 8,5 8,8

So, as we see, we have 36 results which was obvious from first glance, having our nxm theorem telling us we had 6 results on the first throw and another 6 for our second, so thats 6x6=36.

Now, the best part:

You said


What is the probabilty that the sum of the two rolls is a Fibonacci number?

We want (x + y) to equal a Fibonacci Number, right? Let me write some the Fibonacci numbers up to number 16, since our maximum x+y value will be 8+8=16


Fibonacci Sequence
0 1 1 2 3 5 8 13

All right, now let me recall our space S


1,1 1,1 1,2 1,3 1,5 1,8
1,1 1,1 1,2 1,3 1,5 1,8
2,1 2,1 2,2 2,3 2,5 2,8
3,1 3,1 3,2 3,3 3,5 3,8
5,1 5,1 5,2 5,3 5,5 5,8
8,1 8,1 8,2 8,3 8,5 8,8

As we can see, we can have for the each row of S (bear in mind that results satisfacing x+y= Fibonnacci are marked in a darker fashion)
1+1= 2, 1+1= 2, 1+2= 3, 1+3= 4, 1+5= 6, 1+8= 9
1+1= 2, 1+1= 2, 1+2= 3, 1+3= 4, 1+5= 6, 1+8= 9
2+1= 3, 2+1= 3, 2+2= 4, 2+3= 5, 2+5= 7, 2+8= 10
3+1= 4, 3+1= 4, 3+2= 5, 3+3= 6, 3+5= 8, 3+8= 11
5+1= 6, 5+1= 6, 5+2= 7, 5+3= 8, 5+5= 10, 5+8= 13
8+1= 9, 8+1= 9, 8+2= 10, 8+3= 11, 8+5= 13, 8+8= 16

So now all we have to do is count the number of results that satisfies x+y= Fibonacci number, and divide by 36 which is S, our total space.

This yields:

14/36 = 7/18

Which is a high probability, but its logical as well, since our dice has a Fibonacci sequence on each face.

I hope you understood xD

Feel free to correct me, Im more stupid than a geek.

Edited: Found a mistake and corrected.

[X117]

wow havokd ... xd

[Dunzo]

thank you havokd! i am just swamped with work and don't have time to do silly things like these right now. the help is greatly greatly greatly appreciated! (= there will be one every week so stay tuned thanks !

[HavokD]

Nice :P G luck and keep them going! I like solving these kind of problems

[Blade]

I know its off topic but i saw the thread name and thought it said meth problem xD

[HavokD]

I know its off topic but i saw the thread name and thought it said meth problem xD

Lol! Speaking of meth... have you seen Breaking Bad?? (TV series)