Probability Rule

[keep_running]

For the probability rule, why do events have to be mutually exclusive to add up to 1? Isn’t it enough if the events are exhaustive to account for all possibilities in the data set?

 

[cpk123]

events are collectively exhaustive, but what if the events fall into two or more “events” …
then probability will be double counted.
P(A Union B) = P (A) + P(B) - P(A Intersection B)
if the events are not mutually exclusive - then P (A Intersection B) has some value … and then P(A) + P(B) will be more than 1….
kids in school - french and spanish languages are the subjects. Some kids take spanish, some take french and some take BOTH… The Both will make sure that there is some intersection.
I know I am using a contrived example - but hope you get the idea.