Business Mathematics and Statistics · Ch 8 — Descriptive Statistics and Probability
Basic Concepts of Probability — Random Experiments, Sample Space and Events
Basic Concepts of Probability — Random Experiments, Sample Space and Events
The second half of this chapter turns from describing past data to reasoning about uncertain future outcomes — the mathematics of chance itself, which underlies every business decision made under risk (will a new product succeed, will a shipment arrive on time, will a claim be filed).
Foundational Terms
- Random Experiment: a trial whose outcome cannot be predicted with certainty in advance, but whose set of possible outcomes is known — e.g. tossing a coin, rolling a die, drawing a card.
- Sample Space (): the set of all possible outcomes of a random experiment. Tossing a coin: . Rolling a die: .
- Event: any subset of the sample space — a collection of one or more outcomes the experiment might satisfy, e.g. 'an even number' when rolling a die is the event .
The classical definition of probability, used throughout this chapter (which assumes every outcome in the sample space is equally likely):
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A trial with a known set of possible outcomes, but whose actual outcome cannot be predicted with cer …
The set of all possible outcomes of a random ex …
Any subset of the sample space; the event 'occurs' if the experiment's actual outcome lies …
, defined when every outcome of the sample space is equally likely; always satisfies , with for the …