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What is the difference between Independent Events and Disjoint Events?

Independent events means, given the Probability of one event, you cannot say anything about the other.

Suppose there are two events, A and B. They are independent if

$P(A|B) = P(A)$,

i.e. the knowledge that event B has occurred, tell us nothing about the event A.

However, if event A and B are disjoint (or mutually exclusive, they mean the same thing), then

$P(A|B) = 0$,

as A and B cannot occur together, i.e. presence of B tell us that now A cannot occur.

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There are any relation between, dependents event, independent events, and mutually exclusive(Disjoint)events$?$

Dependent events:- An event that affected by the previous events.

For the dependent events, we can take an example of Bag which contains, three red $(3R)$balls and two black$(2R)$ balls.

We want to draw two balls from the bag, what is the probability that both are red(Without replacement)

Without Replacement:- the events are Dependent (the chances change)

Independent Events:- the occurrence of one event does not affect the occurrence of the others e.g if we flip a coin two times, the first time may show a head, but the next time when we flip the coin the outcome will also be heads. From this example, we can see the first event does not affect the occurrence of the next event.

For the independent events, We want to draw two balls from the bag, what is the probability that both are red(With replacement)

With Replacement:- the events are Independent (the chances don't change)

Mutually exclusive events:- two events are the mutually exclusive event when they cannot occur at the same time. e.g if we flip a coin it can only show a head or a tail, not both.

For Mutual exclusive(disjoint) events

NO.
thank you

If A and B are mutually exclusive events then ,A and B are dependent because occurrence of event B restricts occurrence of A and vice versa

check at 18:24 this video

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