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  2. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    In probability theory, the law (or formula) of total probability is a fundamental rule relating marginal probabilities to conditional probabilities. It expresses the total probability of an outcome which can be realized via several distinct events , hence the name.

  3. Bayes' theorem - Wikipedia

    en.wikipedia.org/wiki/Bayes'_theorem

    Once again, the answer can be reached without using the formula by applying the conditions to a hypothetical number of cases. For example, if the factory produces 1,000 items, 200 will be produced by A, 300 by B, and 500 by C. Machine A will produce 5% × 200 = 10 defective items, B 3% × 300 = 9, and C 1% × 500 = 5, for a total of 24.

  4. Binomial distribution - Wikipedia

    en.wikipedia.org/wiki/Binomial_distribution

    In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p).

  5. Conditional probability - Wikipedia

    en.wikipedia.org/wiki/Conditional_probability

    P(A|B) may or may not be equal to P(A), i.e., the unconditional probability or absolute probability of A. If P(A|B) = P(A), then events A and B are said to be independent: in such a case, knowledge about either event does not alter the likelihood of each other. P(A|B) (the conditional probability of A given B) typically differs from P(B|A).

  6. Coupon collector's problem - Wikipedia

    en.wikipedia.org/wiki/Coupon_collector's_problem

    In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...

  7. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    A probability distribution whose sample space ... closed formula for it. [25] One example is shown ... system has a probability measure, and the main problem is the ...

  8. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    Probability is the branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to ...

  9. Birthday problem - Wikipedia

    en.wikipedia.org/wiki/Birthday_problem

    In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.

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