>>11139683first woman you have 1/2 chance of getting hiv and 1/2 chance of getting a healthy child, second woman, you are 50% hiv, 1/2 chance of getting hiv if you don't have it other 1/2 chance of woman being healthy but u have 50% hiv so you have 1/4 healthy child, third woman, you are 75% hiv, 1/2 chance woman has hiv, 1/2 chance she doesnt but you are 75% hiv so you have 1/4 * 1/2 chance, 1/8. if it isnt obvious already this is just 1/2 + 1/4 + 1/8.... 800 times,
if we make nth term out of a sequence that is the sum that adds up every term it would just be 2^n-1/2^n if we put 800 into this we get (holy shit these numbers are massive wait let me put it into python so i get full number instead of standard form) ok im back so we get 6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877375/6668014432879854274079851790721257797144758322315908160396257811764037237817632071521432200871554290742929910593433240445888801654119365080363356052330830046095157579514014558463078285911814024728965016135886601981690748037476461291163877376 children which is pretty close to 1 but not quite there
