Possibility of a sample space containing the following:

In summary, it is not possible for a sample space to contain outcomes that are both independent and mutually exclusive, unless one of the events has a probability of 0. This applies to a single experiment with multiple outcomes.
  • #1
SavvyAA3
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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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  • #2
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)
 
  • #3
Thanks!
 

1. What is a sample space?

A sample space is the set of all possible outcomes of a random experiment. It includes all possible values, events, or observations that can occur in a given situation.

2. Can a sample space contain infinite elements?

Yes, a sample space can contain an infinite number of elements. For example, the sample space for rolling a dice contains six possible outcomes, but the sample space for flipping a coin theoretically contains an infinite number of outcomes.

3. Is it possible for a sample space to have overlapping elements?

Yes, a sample space can have overlapping elements. For example, the sample space for drawing a card from a deck contains 52 possible outcomes, but some cards can have multiple characteristics (e.g. being a red card and a face card).

4. What is the difference between a simple and a compound sample space?

A simple sample space contains only one type of event or outcome, while a compound sample space contains multiple types of events or outcomes. For example, flipping a coin once has a simple sample space (heads or tails), but flipping a coin twice has a compound sample space (HH, HT, TH, TT).

5. Can a sample space contain impossible or unlikely events?

Yes, a sample space can contain impossible or unlikely events. It is important to include all possible outcomes in a sample space, even if some have a very low probability of occurring. This ensures that the sample space is comprehensive and accurate.

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