Probability plays a central role in the important statistical method of hypothesis testing
An event is any collection of results/outcomes of a procedure
A simple event is an outcome/event that cannot be further broken down into simpler components
The sample space for a procedure consists of all possible simple events. That is, the sample space consists of all outcomes that cannot be broken down any further.
3 common approaches to finding the probability of an event:
Law of large numbers: as a procedure is repeated again and again, the relative frequency probability of an event tends to approach the actual probability
The complement of event A, denoted by A bar, consists of all outcomes in which event A does NOT occur
If, under a given assumption, the probability of a particular observed event is very small and the observed event occurs significantly less than or significantly greater than what we typically expect with that assumption, we conclude that the assumption is probably not correct
The actual odds against event A occurring are the ratio P(A bar) / P(A)
The actual odds in favor of event A occurring are the ratio P(A) / P(A bar)
The payoff odds against event A occurring are the ratio of net profit to the amount bet
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