burgerandcheese
Junior Member
- Joined
- Jul 2, 2018
- Messages
- 85
Hi, from what I understand:
When two events A and B are mutually exclusive, then if one event occur, the other event cannot. Or if we draw a Venn diagram, A and B do not intersect.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = P(A) + P(B)
Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of other(s). For example, when selecting 3 students out of a group of 5 students with replacement, then the probability of each trial is the same (it is possible to choose the same student multiple times).
P(A ∩ B) = P(A) * P(B)
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I've done a couple of searches online and I found that "mutually exclusive events are not independent, and independent events cannot be mutually exclusive". I'm frustrated because I still cannot understand why. I imagined it like this: if two events are independent, then they must intersect on the Venn diagram. But for mutually exclusive events, they do not touch. Therefore mutually exclusive events are not independent.
When two events A and B are mutually exclusive, then if one event occur, the other event cannot. Or if we draw a Venn diagram, A and B do not intersect.
P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = P(A) + P(B)
Events are independent if the occurrence of one event does not influence (and is not influenced by) the occurrence of other(s). For example, when selecting 3 students out of a group of 5 students with replacement, then the probability of each trial is the same (it is possible to choose the same student multiple times).
P(A ∩ B) = P(A) * P(B)
--
I've done a couple of searches online and I found that "mutually exclusive events are not independent, and independent events cannot be mutually exclusive". I'm frustrated because I still cannot understand why. I imagined it like this: if two events are independent, then they must intersect on the Venn diagram. But for mutually exclusive events, they do not touch. Therefore mutually exclusive events are not independent.