now because of the random distribution of datait doesn' work out to be exactly the same thing we're talking about probabilities hererememberbut they're in the same ballparkso that makes senseabout versus %close enough now that is different again from ( | )so the probability of both being in your  and buying something is different than the probability of buying something given that you're in your  now let' just do little sanity check here we can check our equation that we saw in the conditional probability section earlierthat said that the probability of buying something given that you're in your  is the same as the probability of being in your  and buying something over the probability of buying something that iswe check if ( | )= ( , )/ (fgmpbu qvsdibtft  this gives us vu sure enoughit does work out if take the probability of buying something given that you're in your  over the overall probabilitywe end up with about %which is pretty much what we came up with originally for ( |fso the equation worksyayalrightit' tough to wrap your head around some of this stuff it' little bit confusingi knowbut if you need togo through this againstudy itand make sure you understand what' going on here 've tried to put in enough examples here to illustrate different combinations of thinking about this stuff once you've got it internalizedi' going to challenge you to actually do little bit of work yourself here conditional probability assignment what want you to do is modify the following python code which was used in the preceding section gspnovnqzjnqpsusboepn sboepntffe upubmt \qvsdibtft \upubm vsdibtft gps@josbohf bhf%fdbef sboepndipjdf qvsdibtf spcbcjmjuz 