Block, SkipCaptcha, Automoderated users, edit, rollback
3,135
edits
Changes
Jump to navigation
Jump to search
Line 7:
Line 7: + + + + + + +
add kolmogorov probability
For example, the probability of a tossed fair coin coming up heads is ½ = 0.5 = 50% because there is one favorable outcome (heads) out of 2 possible outcomes (heads and tails). Another common example is standard deck of 52 playing cards: there are 13 cards in each suit: spades, hearts, clubs and diamonds. After the deck is shuffled thoroughly, the probability that the top card on the deck is a heart is <math>13 / 52 = 1 / 4 = 0.20</math>, or 20%.
For example, the probability of a tossed fair coin coming up heads is ½ = 0.5 = 50% because there is one favorable outcome (heads) out of 2 possible outcomes (heads and tails). Another common example is standard deck of 52 playing cards: there are 13 cards in each suit: spades, hearts, clubs and diamonds. After the deck is shuffled thoroughly, the probability that the top card on the deck is a heart is <math>13 / 52 = 1 / 4 = 0.20</math>, or 20%.
==Formal definition of probability==
Let <math>S</math> be the sample space and <math>E</math> be a [[σ-algebra]] of events. A probability function <math>P\colon E \to \mathbb{R}</math> is a function satisfying the Kolmogorov axioms of probability:
#<math>P(A) \geq 0</math> for all events <math>A \in E</math>
#<math>P(S) = 1</math>
#If <math>\{A_n\}</math> is a countably infinite pairwise disjoint family of events in <math>E</math>, then
<math>P\left(\bigcup_{n=1}^\infty A_n\right) = \sum_{n=1}^\infty P(A_n)</math>
==Empirical vs Theoretical Probability==
==Empirical vs Theoretical Probability==