Maths help

[RizzoTheRat]

My brains not working.

I'm trying to calculate some accumulated probability distributions and need some help.

I have a series of variables where each has an 20% probability of being true and a 80% probability of being false

If I only have 2 variables I can quickly work out that theres a 64% chance of all being false (0.8^2) and 4% than none are false (0.2^2), leaving a 32% chance of only 1 being false. How do I work out the equivilent for n variables, ie the probability of there being 0,1,2,...n falses, without going through it long hand?

And before anyone says it they're not boxes of cats!

[mrmr96]

P(n) = P^n

(or something)

[mrmr96]

Are you saying that the probability of TRUE is always 0.8. And you want to find the probability of "m" trues in any order from "n" events?

[RizzoTheRat]

The probability is constant for the data set yes, but varies between sets.

So I'm after the the probability of M Trues from N events where P is the probabilility a single event being False.

Actually Shrodinger is a good analogy.
P is the probability of a cat in a single box being dead
N is the number of boxes
What's the probability of there being M dead cats?

I can quite easily work it out long hand for a given (lowish) value of N, but I'm struggling with how to work out the number of ways that could occour (eg 6 ways of getting 2 dead cats from 4 boxes)

[RizzoTheRat]

Aha, your binomial coefficient link that now sees to have vanished does the trick.

The probability of there being M dead cats is

N!/((N-M)! x M!) x (1-P)^M x P^(N-M)

that seems to work

Edited by RizzoTheRat on Monday 15th October 17:18

[mrmr96]

Yeah, I took it back down because I wasn't sure. But glad you've got something to work.

[RizzoTheRat]

The important thing is it saves me having to ask the Mrs (she's a maths teacher) how to do it when I get home tonight

[Simpo Two]

RizzoTheRat said:

Actually Shrodinger is a good analogy.

I thought the whole point of the cat was that it didn't have a probability... it's unknown. But I may be wrong.

[mrmr96]

Simpo Two said:

RizzoTheRat said:

Actually Shrodinger is a good analogy.

I thought the whole point of the cat was that it didn't have a probability... it's unknown. But I may be wrong.

Lol yeah, Shrodinger was making a point about something else - but don't confuse the lad!

[RizzoTheRat]

Well I did originally say it wasn't cats

Actually there is still probability involved in the Schrodinger example, its only in a superposition of eigenstates until you open the box, at which point there's a probability the cat is dead. So my example works so long as you open the box

[Caruso]

Dunno, but I read on another thread that the "Top-Heavy Fractions" helpline is now open 24/7.