Simple math question

[LinusKS]

Suppose your probability is 1 out of x occurances.

After x occurances, what is the probability that it's happened?

[Keats13]

So the probability of the event is 1/x.
The probability of it not happening is 1-(1/x)

The probability of it not happening for x consecutive chances is
[1-(1/x)]^x

So the probability that it HAS happened is

1-[1-(1/x)]^x

Example: Event has a probability of 0.5, or 1/2
Probability that it has happened after 2 chances
1-[1-(1/2)]^2 = 1-(1/2)^2 = 1-1/4 = 0.75

For x=10, (event with probability 0.1), the probability that it has happened after 10 chances is
1-[1-(1/10)]^10 = 1-(0.9)^10 = 1-.349 = 0.651

[LinusKS]

Thank you.

Btw, am I right in thinking that equation yields the answer for x happening at least once? In other words, it includes the chance that x happened more than once, right?

[Nottom]

[ QUOTE ]
Btw, am I right in thinking that equation yields the answer for x happening at least once? In other words, it includes the chance that x happened more than once, right?

[/ QUOTE ]

Yes, since its just 1 minus the chance of it not happening at all this includes all the times x happens 2, 3, 4, or x times as well.