Can’t this calculation be done formally, without a script? Like, we’re saying that if you randomly pick a number from 1 to 365 3 times, the number of chances it is not the same day is 1-(1/365)^2. Because there are C(3,N) possible combinations of triplets, the number we’re looking for is (1-(1/365)^2)^C(3,N), right?
For N=64, I get 26%, consistent with your results. To make sure that 2 of them are major, if there is a 30% chance of any single one being major, that probability is 30%^3+3*30%^2 ~ 29%. The end-result would be 26%*29% ~ 7.9%, again consistent with your simulation.
Yes, this can definitely be solved mathematically. The point I wanted to make here by using a simple python simulation, is that sometimes writing a quick script can be easier. You can also easily change the script and make the simulation more and more complex with only a few lines of code (and without having to work out all the math to get to the answer).
Can’t this calculation be done formally, without a script? Like, we’re saying that if you randomly pick a number from 1 to 365 3 times, the number of chances it is not the same day is 1-(1/365)^2. Because there are C(3,N) possible combinations of triplets, the number we’re looking for is (1-(1/365)^2)^C(3,N), right?
For N=64, I get 26%, consistent with your results. To make sure that 2 of them are major, if there is a 30% chance of any single one being major, that probability is 30%^3+3*30%^2 ~ 29%. The end-result would be 26%*29% ~ 7.9%, again consistent with your simulation.
I did not know Carla won so many raffles 😊
Hi Stephane,
Thanks for your question!
Yes, this can definitely be solved mathematically. The point I wanted to make here by using a simple python simulation, is that sometimes writing a quick script can be easier. You can also easily change the script and make the simulation more and more complex with only a few lines of code (and without having to work out all the math to get to the answer).