Sample space I is a term used in probability theory to refer to the set of all possible outcomes of an experiment. It is an important concept that is used to calculate probabilities of various events. In this article, we will discuss the definition of sample space, its components, and the methods used to calculate probabilities.
Definition
Sample space I is a collection of all the possible outcomes of an experiment. It is typically denoted by S and is a subset of the universal set U. All the elements of S represent the outcomes of a single experiment. For example, if we are flipping a coin, the sample space would be S = {Heads, Tails}.
Components
The components of sample space I are the elements of S. These elements are typically denoted by s1, s2, s3, etc. They represent all the possible outcomes of an experiment. For example, if we are rolling a dice, the sample space will be S = {1, 2, 3, 4, 5, 6}.
Calculating Probability
Once the sample space I is defined, we can use it to calculate the probability of an event. The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes in the sample space. For example, if we are rolling a dice, the probability of rolling a four will be 1/6, since there is only one favorable outcome out of the six elements in the sample space.
Conclusion
In conclusion, sample space I is a set of all possible outcomes of an experiment. It is used to calculate the probability of various events. The components of sample space I are the elements of S, which represent all the possible outcomes of an experiment. Finally, the probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space.
References
Konstantopoulos, T. (2016). Introduction to Probability. Retrieved from http://www.probabilitycourse.com/chapter1/1_1_1_sample_space.php
Ross, S. M. (2017). Introduction to Probability and Statistics. New York, NY: W.H. Freeman.
Weisstein, E. W. (2019). Sample Space. Retrieved from https://mathworld.wolfram.com/SampleSpace.html