A sample space in statistics refers to the set of all possible outcomes of a random experiment. It is denoted by the symbol S and is used to calculate the probability of an event occurring.
To identify the sample space in a problem, you need to carefully read the question and list all the possible outcomes. For example, if you are rolling a dice, the sample space would be {1,2,3,4,5,6} as these are all the possible outcomes.
A sample space is the set of all possible outcomes, while an event is a subset of the sample space that satisfies a certain condition. For example, in the rolling dice example, an event could be getting an even number, which would be {2,4,6}.
The probability of an event is calculated by dividing the number of outcomes that satisfy the event by the total number of outcomes in the sample space. For example, if you want to calculate the probability of getting an even number when rolling a dice, it would be 3/6 or 0.5.
Yes, the sample space can change in a problem. It depends on the conditions given in the problem. For example, if you are rolling a dice and are asked to only consider outcomes greater than 4, the sample space would now be {5,6} instead of {1,2,3,4,5,6}.