Probabilities

dr_dan

Would someone be able to tell me of a method that can tell me the answer to the following. Say you have the probability of an event being successful which is p, and you'd like to know how many times you need to repeat the event in order for the probability of getting at least one success to be say, greater than 0.9. Is there a way of doing this? If you could provide a brief explanation, or say a link to a wikipedia page (i couldnt find anything myself) that'd be great.

Alpharius

if we say the number of repitions required is x; and the probability of a single successful event is P(event) then what you want is the number of successive failures where the probability of all of them being failures is equal to 1-0.9

success = P(event)
failure = 1-P(event)
x = repititions
desired probability of success = 0.9
=> desired probability of failure = 0.1

with a little bit of juggling I get

x=ln (0.1)/ln(1-P(event))

and the number of repititions must be greater than or equal to x to get your required success rate

SanderJK

Harlequin is correct, but to show how he reached that point:

Treshhold:



0.1 = (1-p)^x

ln(0.1) = x ln(1-p)

x = ln(0.1) / ln(1-p)

(Clarified this, because someone who is not familiar with this level of chance calculation may not know logarithmic things like ln(a^x) = x ln(a)

dr_dan

' wrote:

-[arlequin;9497805']if we say the number of repitions required is x; and the probability of a single successful event is P(event) then what you want is the number of successive failures where the probability of all of them being failures is equal to 1-0.9

success = P(event)
failure = 1-P(event)
x = repititions
desired probability of success = 0.9
=> desired probability of failure = 0.1

with a little bit of juggling I get

x=ln (0.1)/ln(1-P(event))

and the number of repititions must be greater than or equal to x to get your required success rate

Thanks! That works perfectly, I've got the answer i need now but would you mind telling me what the 'little bit of juggling' was, or at least how you started?

edit: oh right, thanks sander. Thread over i guess, lock plz

Bliss 101

The probability of an event happening at least once is 1 - the probability of it not happening at all. For a series of X repeats, your probability of at least one success is:

1 - (1 - p)^X

For example, if you roll 6-sided die 3 times, your chance of getting a "6" at least once (p = 0.167 for each roll) is 1 - (1 - 0.167)^3 = 42.2%

Since p is presumably known and X can only take integer values, I'd just draw a curve in Excel or this handy tool to find where the function reaches 0.9. For the 6-sided die you'd apparently need to roll 13 times to have a 90% chance of getting at least one "6".