Re: p(A1 U A2 U ...UAk) = p(1) + p(2) + ... + p(k)

Kelvin Thorpe

Do you want to ask if there are Independent and mutually exclusive events?
Simple:
In throwing an ordinary die
____A = to turn up a face with 4 points
____after B = to turn up a face with more than 5 points

INDEPENDENCE deals with the trial, (the *machine* producing the event), MUTUAL EXCLUSIVINESS with the sample space, the set of possible outputs.
Dice (or coins) provide independent trials, ball draws without replacement from urns with finite contents NO. On contrary with replacement we have independence.
The confusion (from unlearned persons) is that how reading the independence condition:

_______p(A|B) = p(A)

they though that concerns the SAME trial (as Bob-Yurra). ABSOLUTMENT NOT, is for two trials, one after the other, A after B be completed. (IMO).

_______licas (Luis A. Afonso)
.