Actually, with the numbers we're talking about, the difference between the two calculations is insignificant.Mortai Gravesend said:Well actually our calculations would give different numbers. Can't just multiply x by 150/7,000,000,000. The proper chance that one will be selected is 150/7,000,000,000*(6,999,999,850/7,000,000,000)^(x-1). Or at least close to that, in actuality we'd need to keep decreasing that denominator with every multiplication. But at 7,000,000,000 that wouldn't matter much if x is only like 5k.The Thinker said:Right. As in, we are both correct.Mortai Gravesend said:Well I was calculating it as 6,999,999,900/7,000,000,000 chance one of the 100 would not get killed. Then putting that to the xth power to give the me the chances one of the 100 would not get killed in x selections.
[facetiousness]But you obviously need to go meet 50 more people.[/facetiousness]
5000*150/7000000000 = 0.000107142857
1-(6999999850/7000000000)^5000 = 0.000107137119
Which are identical answers to 5 significant figures.
Yes, the correct calculation in a case like this is 1-(1-p)^n, but if p and n are small 1-(1-p)^n =~ np.