Talk:Mesa/@comment-139.60.142.196-20171214071828/@comment-25254386-20171215020509

You too are talking about two different things. OP was referring to the 'expected number of runs', while 173.244 above is solving for the 'number of runs to nearly guarantee' each part at least once.

For OP's point, it's just a matter of logic-ing it out. You start with 0 of 3 desired parts, so the chance you will get a part you do not already have is 100% (1 run on average). Now you have 1 of 3 desired parts, so the chance you will get a part you do not already have is 64.93% (1.54 runs on average). Now you have 2 of 3 desired parts, so the chance you will get a part you do not already have is 30.81% (3.25 runs of average). So in total that's 1 + 1.54 + 3.25 = 5.79 &rarr; 5-6 runs.

As for 173.244 above, they're using the method to find the 'nearly guaranteed' number of runs, which you'll see lines up with the "36±9 runs" on the page.
 * 1 - (1 - 0.3872)27 - (1 - 0.3872)27 - (1 - 0.2256)27 ≃ 99.9% chance to obtain all three parts in 27 runs
 * 1 - (1 - 0.3872)36 - (1 - 0.3872)36 - (1 - 0.2256)36 ≃ 99.99% chance to obtain all three parts in 36 runs
 * 1 - (1 - 0.3872)45 - (1 - 0.3872)45 - (1 - 0.2256)45 ≃ 99.999% chance to obtain all three parts in 45 runs