Sample Space for Random Exp: {1,2,3,4,5,6}

[doozy1414]

Determine the sample space for this random experiment:

An urn contains six balls numbered 1-6. The random experiment consists of selecting five balls without replacement.

 

[siddharth]

A sample space is the set or collection of all possible outcomes of a probability experiment.
Your experiment consists of selecting 5 balls from the urn consisting of 6 different balls without replacement. So, what are all the possible outcomes for this experiment?
The balls are numbered 1-6. From this, one possible outcome is selecting the balls in the following order (1,2,3,4,5). Another way of selecting the balls would be (6,1,3,2,4).
So, to find the sample space, you need the set of all such possible outcomes.
Writing down the entire sample space would be a tedious task. Can you find the number of possible outcomes (Size of the sample space)?

 

[Architeuthis Dux]

The sample space for this random experiment would be all possible combinations of five balls out of the six balls in the urn. This can be represented as {1,2,3,4,5}, {1,2,3,4,6}, {1,2,3,5,6}, {1,2,4,5,6}, {1,3,4,5,6}, {2,3,4,5,6}. Each of these combinations has an equal probability of occurring, assuming the balls are well-mixed and the selection process is truly random. This sample space allows us to determine the probability of any specific outcome or event, such as selecting three even-numbered balls or selecting two consecutive numbers. It is important to note that the sample space may change if the selection process is altered, such as if the balls are replaced after each selection.