Why are mutually exclusive events dependent and not independent (statistics)
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Why are mutually exclusive events dependent and not independent (statistics)

[From: ] [author: ] [Date: 11-05-30] [Hit: ]
thus the total sample space has decreased.Hence we can say that thefirst event has influenced the result of the second!!Hope this helps!......

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Ten red balls, ten blue balls.
First draw, P(red) = 50%
once that draw is done (let's assume I picked red), and if I do not put that red ball back in the bag, then the probability on the second draw is
P(red) = 47.4%
this is NOT an independent event.

If I had picked blue on the first draw, then the probability of red on the second draw is 52.6%

In either case, it is no longer 50%. The outcome of the first draw affects the second draw, therefore the second draw is NOT independent from the first draw (even though, in this case, it is not a mutually exclusive event).

Mutually exclusive just happens to be an extreme case.

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I shall state one example for this:
Say u have one bag containing 5 Red balls and 5 Black balls.
Now u are asked to pick one ball at random without replacement.
Probablity of picking the red ball first say will be 5/10
now when u ask for the probablity of again getting a red ball is 4/9 or the black ball is 5/9.
thus the total sample space has decreased.
Hence we can say that the first event has influenced the result of the second!!

Hope this helps!
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