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4.1-4.2

# 4.1-4.2 - Probability Randomness;Probabilitymodels...

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Probability Randomness; Probability models

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Randomness and probability Probability models: sample spaces, events Assigning probabilities: finite number of outcomes Basic probability rules
Random phenomena vs deterministic phenomena

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A phenomenon is random if individual outcomes are uncertain, but there is nonetheless a regular distribution of outcomes in a large number of repetitions. Randomness and probability The probability of any outcome of a random phenomenon can be interpreted as the proportion of times the outcome would occur in a very long series of repetitions ( long-term relative frequency ).
Coin toss The result of any single coin toss is random. But the result over many tosses is predictable, as long as the trials are independent (i.e., the outcome of a new coin flip is not influenced by the result of the previous flip). First series of tosses Second series The probability of heads is 0.5: approximate proportion of times you get heads in many repeated trials.

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A probability model describes mathematically the outcome of a random phenomenon. It consists of two parts: 1) S = Sample Space : This is a set, or list, of all possible outcomes of a random phenomenon. 2) A way of assigning probability to each possible outcome. Probability models Example: Probability Model for a Coin Toss : S = {Head, Tail} Probability of heads = 0.5 Probability of tails = 0.5
Probabilities range from 0 to 1. Because some outcome must occur in every trial, the sum of the probabilities of all possible outcomes must be exactly 1. If we have a biased coin, say P (head) = 0.3, then P (tail) = 0.7 If P (head) = 2 P (tail), then P (head) = 2/3

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We can assign probabilities either: empirically from our knowledge of numerous similar past events Mendel discovered the probabilities of inheritance of a given trait from experiments on peas without knowing about genes or DNA.
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