Often times there will be uncertainity: Where we might believe somethin with some probability but not entirely for certain.
Consider predicting the weather: you can infer the weather going to be tomorrow using some probability and then calculate the likelihood of this particular event. Therefore, probability refers ti the idea of a possible world: like, 6 possible worlds that could result into being true, P(w).
There are couple of basic axioms of probability that become relevent how we deal with it:
-> Every probability value must range between 0 and 1.
-> Adding all the values of the possible probabilities for all the possible worlds gives us 1.
Unconditional probability: some fact about the world with no evidence of it in the world.
Conditional probability: Degree of belief in a proposition given some evidence that has already been revealed, P(a | b): This is the probability that a is true.
P(disease | test results): Knowing the probability of a patient having that particular disease from the test results revealed.
How do we calculate conditional probability? P(a | b) = P(a and b) / P(b)
P(b), we only care for the worlds where b is true.
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Random Variable Roll : {1, 2, 3, 4, 5, 6}
Weather : {sun, cloud, rain, wind, snow}
Traffic : {none, light, heavy}
Flight: {on time, delayed, cancelled}
Probability distribution: takes a random variable and gives the probability for each of the possible values for each domain.
This can also represented as a vector. So, the notation is P(Flight) = <0.6, 0.3, 0.1> Where 1st value is the probability that the flight is on time, 2nd is delayed, 3rd is cancelled.
Inclusion-Exclusion
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