. Probability in the real world. In real life, there are often situations where there are severalpossible outcomes but which one will occur is unpredictable in some way. For example, when wetoss a coin, we may get heads or tails. In such cases we use words such as probability or chance,event or happening, randomness etc. What is the relationship between the intuitive and mathematicalmeanings of words such as probability or chance?In a given physical situation, we choose one out of all possible probability spaces that we thinkcaptures best the chance happenings in the situation. The chosen probability space is then called amodel or a probability model for the given situation. Once the model has been chosen, calculation ofprobabilities of events therein is a mathematical problem. Whether the model really captures thegiven situation, or whether the model is inadequate and over-simplified is a non-mathematicalquestion. Nevertheless that is an important question, and can be answered by observing the reallife situation and comparing the outcomes with predictions made using the model2.Now we describe several “random experiments” (a non-mathematical term to indicate a “reallife” phenomenon that is supposed to involve chance happenings) in which the previously givenexamples of probability spaces arise. Describing the probability space is the first step in any probability problem.
Variance and standard deviation of a population