The spelling of "sample space" is straightforward once you understand the phonetic transcription of each word. "Sample" is spelled /ˈsæmpəl/ with the first syllable stressed and pronounced as "sam", followed by the short vowel "pul". "Space" is spelled /speɪs/ with a diphthong at the beginning pronounced as "spey", and ending with the voiceless "s" sound. Together, the two words create the concept of the possible outcomes in a statistical experiment. The sample space is the set of all possible outcomes in a trial.
The sample space is a fundamental concept in probability theory and is used to describe all possible outcomes of a random experiment or process. It refers to the set of all possible outcomes or results that can occur when conducting an experiment or observation.
In simpler terms, the sample space is like a container that holds all the possible results of an event or experiment. It represents the full range of possibilities that can occur when performing a specific task or observing a particular phenomenon.
For example, consider flipping a fair coin. The sample space in this case consists of two possible outcomes: heads or tails. It is denoted by the set {H, T}, where H represents the event of getting heads and T represents the event of getting tails.
Similarly, rolling a six-sided die would have a sample space denoted by the set {1, 2, 3, 4, 5, 6}, as these are the possible outcomes that can occur.
The sample space is essential in understanding probability as it enables us to determine the likelihood of each outcome occurring. By analyzing the sample space and assigning probabilities to each outcome, we can calculate the probability of specific events or combinations of events.
The term "sample space" has its etymology rooted in probability theory and statistics. The word "sample" comes from the Old French "essample" or "exemplum", which means an example or a pattern. It eventually entered Middle English as "sample" with a similar meaning.
The word "space" originated from the Latin "spatium", meaning an area or extent. It further developed in Old French as "espace", still carrying the sense of an area or a room.
When the two words are combined, "sample space" refers to the set of all possible outcomes or elements in a statistical or probabilistic experiment. The term is used to describe the collection or space of all possible sample points or events in a particular context.