Sample Spaces Worksheets

What Are Statistical Sample Spaces? In statistics, we define sample space as the set of all the possible results of an experiment. The number of outcomes or results present in a sample space depends on the random experiment. In case a sample space has a finite or set number of outcomes, then that sample space is known as finite or discrete. In sample space, events are defined as the subset of all the likely outcomes. We represent sample space by using a symbol 'S'. We enclose a sample space of a random experiment with a curly bracket {}. Most people often confuse sample space and the possible outcomes when we write sample space of any given experiment we write {1, 2, 3, 4, 5, 6}. However, when we are to write the possible outcomes, it can be written as a set of odd outcomes {1, 3, 5}, or even outcomes {2, 4, 6}. Outcomes can be random, but sample space is the universal set for a particular experiment. If we consider an experiment of the coin toss, we will get only two possible outcomes, that is head and tail. Hence, the sample space of a coin toss will be written as: Sample Space (S) = {Head, Tail} or {H, T}. However, the set is different when we flip two coins. Let H1 and T1 be the outcomes of the first coin, and H2 and T2 be the outcomes of the second coin. The possible outcomes can be written as: Sample Space (S) = {(H1, H2), (H1, T2), (T1, H2), (T1, T2)}.