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  2. Bayes' theorem - Wikipedia

    en.wikipedia.org/wiki/Bayes'_theorem

    Within these three, there are two scenarios in which the patient carries the mutant allele. Thus the prior probabilities are 2 ⁄ 3 and 1 ⁄ 3. Next, the patient undergoes genetic testing and tests negative for cystic fibrosis. This test has a 90% detection rate, so the conditional probabilities of a negative test are 1/10 and 1.

  3. Probability distribution - Wikipedia

    en.wikipedia.org/wiki/Probability_distribution

    The pmf allows the computation of probabilities of events such as (>) = / + / + / = /, and all other probabilities in the distribution. Figure 4: The probability mass function of a discrete probability distribution. The probabilities of the singletons {1}, {3}, and {7} are respectively 0.2, 0.5, 0.3. A set not containing any of these points has ...

  4. Probability - Wikipedia

    en.wikipedia.org/wiki/Probability

    The probabilities of rolling several numbers using two dice. 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.

  5. Birthday problem - Wikipedia

    en.wikipedia.org/wiki/Birthday_problem

    The goal is to compute P(B), the probability that at least two people in the room have the same birthday. However, it is simpler to calculate P(A′), the probability that no two people in the room have the same birthday. Then, because B and A′ are the only two possibilities and are also mutually exclusive, P(B) = 1 − P(A′).

  6. Joint probability distribution - Wikipedia

    en.wikipedia.org/wiki/Joint_probability_distribution

    Each of the four inner cells shows the probability of a particular combination of results from the two draws; these probabilities are the joint distribution. In any one cell the probability of a particular combination occurring is (since the draws are independent) the product of the probability of the specified result for A and the probability ...

  7. Chain rule (probability) - Wikipedia

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

    In probability theory, the chain rule [1] (also called the general product rule [2] [3]) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities.

  8. Distribution of the product of two random variables - Wikipedia

    en.wikipedia.org/wiki/Distribution_of_the...

    A product distribution is a probability distribution constructed as the distribution of the product of random variables having two other known distributions. Given two statistically independent random variables X and Y , the distribution of the random variable Z that is formed as the product Z = X Y {\displaystyle Z=XY} is a product distribution .

  9. Law of total probability - Wikipedia

    en.wikipedia.org/wiki/Law_of_total_probability

    [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 alternatives" in the continuous case. [5] This result is given by Grimmett and Welsh [6] as the partition theorem, a name that they also give to the related law of total expectation.