Why can disjoint events never be independent? (this is refering to probability)?

Answer 1

The first person got it wrong; the second person gave the correct reason. Independence and mutual exclusiveness cannot occur together unless P(A) or P(B) equals 0 (a trivial case). For if neither P(A) nor P(B) is 0 then P(A)P(B) is positive. But independence implies P(A intersection B) = P(A)P(B) so P(A intersection B) is positive. But that means events A and B are not disjoint (i.e. mutually exclusive) since there is positive probability that both A and B occur--that is, A intersection B is not empty.

Answer 2

Intuitively, they can't be independent, because the occurrence of A certainly affects the probability of B, in fact it makes B impossible.

Given two disjoint events A and B, each with a positive probability, the probability of B occurring given that A has already occurred is 0, since they can't occur together.

The condition for independence is
P(A&B) = P(A)*P(B), but the left side is 0 and the right side is positive.

Answer 3

"both" will always be "both"?!?!? both of the same sex? (the est. probability of boy or girl doesn't change, so either circumstance would work out correctly) well you can estimate that as a 50-50 probability. the definition is strange as the previous result can tell us thing about the second result but.... they are independent.... dependent would be if the 50%-50% probabilities changed whether or not they had a boy or girl the first time. Even though having the same sex kids over and over (consecutively) in normal modern day human parents (in other words it's not "supposed" to be like that) would have a higher probability of having a kid of the other sex, it supposedly doesn't change things. A bag of marbles or food may be a better example. Do you keep the food or put it back hoping for something else?

Answer 4

Are you sure you have that right? Disjoint events can never occur together so it would seem that they are fundamentally independent.