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diff --git a/sannolikhet/Probability calculation techniques.md b/sannolikhet/Probability calculation techniques.md new file mode 100644 index 0000000..0b0efdf --- /dev/null +++ b/sannolikhet/Probability calculation techniques.md @@ -0,0 +1,16 @@ +A proper definition would probably (hah) use the [[Kolmogorov axioms]]. + +Intuition: probability is "chance". However: something like 50% is not exact. If +something has the probability 50% we don't expect it to happen exactly 50 times +out of 100 tries. Rather, we expect + +$$\lim_{n \rightarrow \infty} \mathrm{N}(\mathrm{heads}) = 50\% \cdot \mathrm{N}(n \ \mathrm{throws})$$ + +# Some rules + +$$P(S) = 1$$ +$$P(\phi) = 0$$ +$$P(A') = 1 - P(A)$$ +$$P(A_1 \cup A_2 \cup ...) = P(A_1) + P(A_2) + ...$$ +$$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ +$$P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A \cap B) - P(B \cap C) - P(A \cap C) + P(A \cap B \cap C)$$ |