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**Unformatted text preview: **11/8/10 1 Probability Basics Lecture 17 Acting under Uncertainty • Probabilitistic Algorithms • Statistical Data Mining • In Machine Learning, probabilities represent an agent’s beliefs in situations when it is not possible to reach a deFnite decision. • Computational Biology Defnitions: • A Sample Space is a set of all possible outcomes of an experiment. • An event is a subset of the sample space. • Sometimes outcomes are referred to as atomic events. • Examples… • Outcomes of a penny toss. S={H,T} • The number of tosses of a penny it takes to toss a heads. S={1,2,3,…} • The amount of dosage it takes for a patient to react positively. S=(0, ∞ ) 11/8/10 2 • Proposition 2: P(E ∪ F) = P(E) + P(F) - P(E ∩ F) • Two fair dice are rolled. What is the probability of rolling doubles or a 6? • Two fair dice are rolled. What is the probability of rolling doubles or a 6?...

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