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Statistics Question

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Numsgil:
Yeah shvarz, this is the flip side.

Say you want the chance of a mutated youngster to be 1 in 36.  I want you to be able to enter 1 in 36 and have the program scale all the mutation probabilities for you automatically.

shvarz:
What I would need to know is whether B, C, D and E are independent events or if they are exclusive.  The solution will be different in the following two scenarios:
1) You throw a dice once and look at the number that comes out.  B is 1, C is 2, D is 3 and E is 4.
2) You throw a dice 4 times and B is "6 comes out on first try", C is "6 comes out on second try", D is "6 comes out on third try" and E is "6 comes out on fourth try".

See what I mean?  We need to know what are events B, C, D, E.

I am also assuming that your event A is probability that any of these four events would happen.

Numsgil:
They are independant.  If they were exlcusive, you're original answer would work.

I'm solving the case for A = B or C right now.  Maybe I can see a pattern.

shvarz:
Oh, OK.

Here is an easier way to do that:

Say I type in "1 in 36".  This gives you the frequency of any mutation happening in the offspring: 1/36.

Then you have the ratios between different kinds of mutations.  These are either set up by the user or are at some default ratios.  Say Insertion:Deletion:Substitution is 1:1:3
Then you take the total of these ratios: 1+1+3 and normalize all frequencies to that.  
So the frequncy of Insertion is 1/36 x 1/5= 1/180
Deletion is the same: 1/180
Substitution is 1/36 x 3/5=1/60

Would that work?

Numsgil:
No, that won't work.

In this case, the difference is .0002155 (or roughly 1 in 4639).  Very tiny and quite negligable.

However, as you increase the number of mutation fields you're editing this will increase.  Once you hit 16 it becomes quite noticable.

Here's the solution for a 2 mutation field case:
Ai = initial A
Bi = initial B
Af = final A, what we're trying to find, = Ai*Bf/Bi
Bf = final B, what we're trying to find

Bf = (Ai+Bi)/Bi +- sqrt( ((Ai+Bi)/Bi) ^2 - 4(Ai/Bi)(New global probability))
--------------------------DIVIDED BY----------------------------------------------
2(Ai/Bi)

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