our upubmt dictionary is telling us how many people are in each age bracketand it' pretty evenly distributedjust like we expected the amount purchased by each age group is in fact increasing by ageso -year-olds only bought about , things and -year-olds bought about , thingsand overall the entire population bought about , things let' use this data to play around with the ideas of conditional probability let' first figure out what' the probability of buying something given that you're in your the notation for that will be ( |fif we're calling purchase eand as the event that you're in your now we have this fancy equation that gave you way of computing ( |fgiven ( , )and ( )but we don' need that you don' just blindly apply equations whenever you see something you have to think about your data intuitively what is it telling usi want to figure out the probability of purchasing something given that you're in your well have all the data need to compute that directly &gmpbu qvsdibtft gmpbu upubmt have how much stuff -year-olds purchased in the purchases[ bucketand know how many -year-olds there are so can just divide those two numbers to get the ratio of year-old purchases over the number of -year-olds can then output that using the print commandqsjou  qvsdibtf]  & end up with probability of purchasing something given that you're in your of being about % qvsdibtf] note that if you're using python the print command doesn' have the surrounding bracketsso it would beqsjou qvsdibtf]  &if want to find ( )that' just the probability of being overalli can take the total number of -year-olds divided by the number of people in my datasetwhich is , gmpbu upubmt qsjou    againremove those brackets around the print statement if you're using python that should give the following output  