Scenario Mystery Car breakdowns You work for (DLG) and you notice an increase in new cars breaking down in their first year on the road. To put a stop to the disruption this is causing our customers, and the claims on DLG insurance policies, you set out to identify what is causing these breakdowns. You have a list of new vehicles that our customers bought in ‘new_cars.csv’, as indicated in that file some of these have broken down. You also have a list of suspect parts that carmakers have recently started using: ‘suspect_car_parts.csv’: some of these parts are causing the breakdowns.

car_name,is_broken_down
Solara, TRUE
Fairmont,FALSE
Vision,FALSE
Stanza,FALSE
Laser,TRUE
Sable,TRUE
Impala,FALSE
Oasis,FALSE
Intrepid,FALSE
Ascender,FALSE
Lucerne,FALSE
Cutlass,TRUE
Previa,FALSE
Summit,FALSE
Hunter,TRUE
Sunbeam,FALSE
Cube,FALSE
Beretta,FALSE
Reatta,TRUE
Cabrio,FALSE

car_name, part_name
Ascender,air conditioner
Ascender,computer
Ascender,power brakes
Ascender,dashboard
Beretta,internal combustion engine
Beretta,power brakes
Cabrio,pedal
Cabrio,navigation system
Cube,reverse light
Cube,brake pedal
Cutlass,radio
Cutlass,turbo charger
Cutlass,suspension
Cutlass,power brakes
Fairmont,starter
Fairmont,computer
Hunter,cooling system
Hunter,muffler
Hunter,rear window defroster
Hunter,suspension
Hunter,computer
Impala,windshield wiper
Impala,bumper
Intrepid,muffler
Intrepid,bumper
Laser,fan belt
Laser,turbo charger
Laser,warning light
Laser,pedal
Laser,suspension
Lucerne,cooling system
Lucerne,fan belt
Lucerne,air conditioner
Lucerne,internal combustion engine
Lucerne,power brakes
Oasis,ignition
Previa,windshield wiper
Previa,fan belt
Previa,bumper
Reatta,turbo charger
Reatta,brake pedal
Reatta,suspension
Sable,cooling system
Sable,fan belt
Sable,automatic transmission
Sable,turbo charger
Sable,pedal
Sable,suspension
Sable,internal combustion engine
Solara,rear window defroster
Solara,turbo charger
Stanza,bumper
Stanza,warning light
Summit,bumper
Summit,suspension
Summit,power brakes
Sunbeam,chrome trim
Vision,muffler

Question

One of the things we could try is to calculate for every suspect part how often they are installed in vehicles, and how often those vehicles have broken down. A higher share of cars breaking down containing a particular part may be suspicious. However, if a part was only installed in one car that broke down it may have just been unlucky, but if a part is installed in several cars and almost all those cars had breakdowns then that is very suspect. A way to quantify how suspicious it is for a part to be installed in a certain number of cars on which a certain number of breakdowns occur is to use the binomial distribution.

The binomial distribution shows the probability Pr(k) of getting exactly k successes in n independent chance events each with a probability of success of p.

What could p be in our case? Please explain your thinking.