# probability of 3 in a row

#### Insight10

##### New Member
Hi the probability of 1 occurance is about 1 in 10 what i would like to calculate is the probability of 3 of these happening in a row at any time across 500 trys .

If it happens twice but not 3 then we are reset to 0 so it has to be 3 in a row at any point in 500 trys

I tried to calculate as a binomial distribution but got a odd result

Thank you

#### katxt

##### New Member
Try a simulation. It looks like about a 60% chance of at least one run of three in 500 tries. Any help?

#### Insight10

##### New Member
Try a simulation. It looks like about a 60% chance of at least one run of three in 500 tries. Any help?
Hi sorry not clear, did you run a simulation and it come out at 60%?

Yes if reasonably accurate then this is fine thank you

#### katxt

##### New Member
I did do a quick simulation but I have just done it again more thoroughly, and this time got 35%+/- 1%. Sorry about that, chief. It may pay to do your own.
As a rough guide, there are about 500 chances, each of which is about 0.001 so the expected number is 0.05. If you approximate with the poisson distribution you get p(1 or more triple) = 1 - e^-0.05 which is about 39%