EntropySink

Technical & Scientific => Programming => Topic started by: Mike on November 18, 2013, 01:20:37 PM

Title: Probability of one success out of multiple independent events
Post by: Mike on November 18, 2013, 01:20:37 PM

This is more of a stats question that programming but...

I have events that produce either A or B.  Each day all the events are reset and the user can redo them.  Each event has a different chance of producing A (otherwise it produces B).  Trying to figure out the chances of A being produced once for a given day.  I know how to calculate the chance that at least 1 A is produced but not sure how to check for a particular amount.

Right now my chances are 10%, 10%, 20%, 30%, 40%, 50%, 60%, 70% which almost guarantees at least 1 A but it is producing too many As.

Anyone know the equations?

Title: Re: Probability of one success out of multiple independent events
Post by: Perspective on November 18, 2013, 01:57:00 PM

The chance of one and only one A? It's the prob event i produces A times the prob that all others produce B, summed over all i.

Title: Re: Probability of one success out of multiple independent events
Post by: hans on November 18, 2013, 01:58:18 PM

Something like this?

http://www.mathsisfun.com/data/probability-events-independent.html

or maybe better

https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/compound-probability-of-independent-events

Title: Re: Probability of one success out of multiple independent events
Post by: Mike on November 18, 2013, 02:16:23 PM

Quote from: Perspective on November 18, 2013, 01:57:00 PM

The chance of one and only one A?

Correct

Quote

It's the prob event i produces A times the prob that all others produce B, summed over all i.

Ah, so no nice easy spreadsheet equation?  Gotta do it bit by bit?

Quote from: tgm on November 18, 2013, 01:58:18 PM

Something like this?

http://www.mathsisfun.com/data/probability-events-independent.html

or maybe better

https://www.khanacademy.org/math/probability/independent-dependent-probability/independent_events/v/compound-probability-of-independent-events

Quote from: tgm on November 18, 2013, 02:08:18 PM

I think it's ~98.367% likely of getting A to happen.

Yeah, already got that part.  But that is the probability of A happening not the probability of A happening only once.

What I'm seeing from actual results is many people are getting A three times in a day which makes sense as the last three events have good odds of producing A.  I want to try and manipulate the numbers so that the chance of A happening is good while limiting the number of times A happens.

Note: Forgot one event with 80% probability which takes the probability of A happening at least once to over 99%

Title: Re: Probability of one success out of multiple independent events
Post by: Mike on November 18, 2013, 02:28:35 PM

ok, so looks like there is a 3.39% chance of A only happening once.  Hmmm need to relook at these numbers.

edit: Spreadsheet error gave wrong value

Title: Re: Probability of one success out of multiple independent events
Post by: charlie on November 19, 2013, 05:42:29 PM

I get 10.45%.



Oh, wait.. you added one more with 80% chance. Yeah, 3.397%.