what 've done here is 've taken the original snippet of code for creating our dictionary of age groups and how much was purchased by each age group for set of , random people instead of making purchase probability dependent on agei've made it constant probability of now we just have people randomly being assigned to an age groupand they all have the same probability of buying something let' go ahead and run that now this timeif compute the ( | )that isthe probability of buying something given that you're in your ti come up with about &gmpbu qvsdibtft gmpbu upubmt qsjou  qvsdibtf]  & qvsdibtf] if compare that to the overall probability of purchasingthat too is about gmpbu upubm vsdibtft qsjou  vsdibtf  vsdibtf  can see here that the probability of purchasing something given that you're in your  is about the same as the probability of purchasing something irrespective of your age (that isp( |fis pretty close to ( )that suggests that there' no real relationship between those two thingsand in facti know there isn' from this data now in practiceyou could just be seeing random chanceso you' want to look at more than one age group you' want to look at more than one data point to see if there really is relationship or notbut this is an indication that there' no relationship between age and probability of purchase in this sample data that we modified sothat' conditional probability in action hopefully your solution was fairly close and had similar results if notgo back and study my solution it' right there in the data files for this bookconditionalprobabilitysolution ipynbif you need to open it up and study it and play around with it obviouslythe random nature of the data will make your results little bit different and will depend on what choice you made for the overall purchase probabilitybut that' the idea and with that behind uslet' move on to bayestheorem