Talk:A Study in the Dubious Meiho-sou/@comment-32751163-20190515092212/@comment-29893250-20190515180844

I haven't checked the math and don't plan to but it should look like this. You just do it in much shorter form when solving. First roll. 7/1000 chance to get Jalter. To get it by roll 2, you already had a chance to have gotten it on the first so you only have a 99.3% chance of whether the second roll matters so (99.3x0.007)/0.993. This repeats till you hit the 960th roll. You add them all up and end up with the total chance to have pulled at least 1 Jalter in said quartz. Not accounting for stuff like 10 roll guaranteed servant and guaranteed 4+ star card. At least that's what it'd look like doing it forwards to get the idea of how you'd theoretically calculate it.

To actually do it like a sane person, there's an easier way to do it. What's the chance of not getting a Jalter? 0.993. How many times do you have to do that in a row to be that unlucky? 960. So we multiply .993 by itself 960 times. (0.993)^960 = 0.0012. This means that there's a 0.12% chance for you to have not pulled a Jalter in 960 pulls. We reverse the statement around and can say that you have a 99.88% chance to pull at least 1 Jalter within 960 rolls.

Also, pulling another SSR in there doesn't make the calculation void. It either is a Jalter or it isn't a Jalter.