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  • Probability: Are disjoint events independent? [duplicate]
    Two disjoint events can never be independent, except in the case that one of the events is null Essentially these two concepts belong to two different dimensions and cannot be compared or equaled Events are considered disjoint if they never occur at the same time
  • Joint disjoint and dependent independent events
    Disjoint means the two events are mutually exclusive -- if one happens than the other can't happen Independent means if one happens it doesn't affect whether or not the other happens You can't simultaneously prevent the other from happening and also not affect whether it happens Disjoint implies dependent
  • Difference between disjoint and independent events
    $\begingroup$ Two disjoint events are necessarily mutually exclusive, and if they also have positive probabilities then they must be dependent $\endgroup$ – ryang Commented Apr 3, 2022 at 12:39
  • Are all disjoint events dependent? - Mathematics Stack Exchange
    $\begingroup$ Disjoint events are definitely not independent, you are right: knowing that one happens prevents the other from happening, so they are not independent $\endgroup$ – Randall Commented Jan 24, 2018 at 19:04
  • What is the difference between mutually independent and pairwise . . .
    Mutual independence: Every event is independent of any intersection of the other events Pairwise independence: Any two events are independent
  • What are some examples of the fact disjoint events are dependent?
    The two events, having fur and breathing through gills, are disjoint and not independent Another example is A="The person is blind since birth" and B="The person is a fighter pilot" However, bear in mind that probability is a mathematical abstraction, while the real world is, well, real
  • terminology - Why are two disjoint events defined to be independent if . . .
    So if you have two disjoint events where at least one has probability $0$, then they are independent It's a degenerate still a degenerate example, so what you end up with is something that doesn't have a particularly meaningful interpretation in a qualitative discussion - but, as mentioned in the answer, this can sometimes be a helpful tool in
  • Whats the difference between MUTUALLY EXCLUSIVE and PAIRWISE DISJOINT?
    Can we say that two PAIRWISE DISJOINT events are not INDEPENDENT as well？ If these two concepts are different (actually my teacher told me they are), could you please give me an example that two events are MUTUALLY EXCLUSIVE but not PAIRWISE DISJOINT, or they are PAIRWISE DISJOINT but not MUTUALLY EXCLUSIVE Thank you for your help
  • probability - Can two independent events be disjoint? - Mathematics . . .
    $\begingroup$ The statements “disjoint events with positive probability are not independent” and “independent events with positive probability are not disjoint” are equivalent statements You have proven the first statement, therefore the second one is true $\endgroup$
  • How can you visualize Independence with Venn Diagrams?
    It's not feasible to represent independence Most people think drawing Venn Diagrams that are disjoint demonstrates independence, but that is false If two events are disjoint, they are inherently dependent Because if I know A occurs, I know B cannot occur and vice versa So what about the opposite: drawing Venn Diagrams that intersect?





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