Possibility of a sample space containing the following:

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SUMMARY

The discussion clarifies that a sample space cannot contain outcomes that are both independent and mutually exclusive within a single probability experiment. It establishes that mutually exclusive events have a joint probability of zero, denoted as P(A*B)=0, while independent events maintain the relationship P(A*B)=P(A) x P(B). The only scenario where these two concepts converge is when one of the events has a probability of zero.

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[SOLVED] Possibility of a sample space containing the following:

Will it ever be possible for a sample space (the set of all possible outcomes of a probability experiment) to contain outcomes that are both independent of each other but in fact also mutually exclusive?

Please note I am considering one experiment and not many. Also note I am considering this one experiment to consist of several outcomes.

Your help would be greatly appreciated.
 
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No. Mutually exclusive P(A*B)=0. Independent P(A*B)=P(A)xP(B). The only time they are the same is when one of the events has 0 probability. (* denotes intersection)
 
Thanks!
 

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