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  2. Conditional probability - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability

    However, the conditional probability P(A|B 1) = 1, P(A|B 2) = 0.12 ÷ (0.12 + 0.04) = 0.75, and P(A|B 3) = 0. On a tree diagram, branch probabilities are conditional on the event associated with the parent node. (Here, the overbars indicate that the event does not occur.) Venn Pie Chart describing conditional probabilities

  3. Conditional probability distribution - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability...

    Then the unconditional probability that = is 3/6 = 1/2 (since there are six possible rolls of the dice, of which three are even), whereas the probability that = conditional on = is 1/3 (since there are three possible prime number rolls—2, 3, and 5—of which one is even).

  4. Buffon's needle problem - Wikipedia

    en.wikipedia.org/wiki/Buffon's_needle_problem

    For simplicity in the algebraic formulation ahead, let a = b = t = 2l such that the original result in Buffon's problem is P(A) = P(B) = ⁠ 1 / π ⁠. Furthermore, let N = 100 drops. Now let us examine P(AB) for Laplace's result, that is, the probability the needle intersects both a horizontal and a vertical line. We know that

  5. Conditioning (probability) - Wikipedia

    en.wikipedia.org/wiki/Conditioning_(probability)

    In this sense, "the concept of a conditional probability with regard to an isolated hypothesis whose probability equals 0 is inadmissible." (Kolmogorov [6]) The additional input may be (a) a symmetry (invariance group); (b) a sequence of events B n such that B n ↓ B, P ( B n) > 0; (c) a partition containing the given event. Measure-theoretic ...

  6. Conditional event algebra - Wikipedia

    en.wikipedia.org/wiki/Conditional_event_algebra

    Thus the conditional probability P(B |A) is turned into simple probability P(B → A) by replacing Ω, the sample space of all ordinary outcomes, with Ω*, the sample space of all sequences of ordinary outcomes, and by identifying conditional event A → B with the set of sequences where the first (A ∧ B)-outcome comes before the first (A ∧ ...

  7. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    Therefore, the probability distribution function of the position of a particle is described by () = | (,) |, probability that the particle's position x will be in the interval a ≤ x ≤ b in dimension one, and a similar triple integral in dimension three. This is a key principle of quantum mechanics.

  8. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    The term law of total probability is sometimes taken to mean the law of alternatives, which is a special case of the law of total probability applying to discrete random variables. [ citation needed ] One author uses the terminology of the "Rule of Average Conditional Probabilities", [ 4 ] while another refers to it as the "continuous law of ...

  9. Chain rule (probability) - Wikipedia

    en.wikipedia.org/wiki/Chain_rule_(probability)

    This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.

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