Search
- Filter Results
- Location
- Classification
- Include attachments
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/04%3A_Discrete_Random_Variables/4.01%3A_Hypergeometric_DistributionThis page discusses the hypergeometric probability distribution, used when probabilities change with each draw, such as drawing cards from a deck without replacement. It details the formula for calcul...This page discusses the hypergeometric probability distribution, used when probabilities change with each draw, such as drawing cards from a deck without replacement. It details the formula for calculating probabilities of specific outcomes, exemplified by drawing two aces in a poker hand. The page also outlines the conditions for applying the hypergeometric distribution and includes an example of calculating the probability of selecting gumdrops from a mix of candies.
- https://stats.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Ikeda)/04%3A__Sets/4.03%3A_Venn_DiagramsTo visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called Venn D...To visualize the interaction of sets, John Venn in 1880 thought to use overlapping circles, building on a similar idea used by Leonhard Euler in the 18th century. These illustrations now called Venn Diagrams.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Lies_Damned_Lies_or_Statistics_-_How_to_Tell_the_Truth_with_Statistics_(Poritz)/04%3A_Probability_Theory/4.01%3A_New_PageSimilar reasoning tells us both that \[P(B)=P(A\cap B)+P(A^c\cap B)\] and that \[A\cup B=\left(A\cap B^c\right)\cup\left(A\cap B\right)\cup\left(A^c\cap B\right)\] is a decomposition of \(A\cup B\) in...Similar reasoning tells us both that \[P(B)=P(A\cap B)+P(A^c\cap B)\] and that \[A\cup B=\left(A\cap B^c\right)\cup\left(A\cap B\right)\cup\left(A^c\cap B\right)\] is a decomposition of \(A\cup B\) into disjoint pieces, so that \[P(A\cup B)=P(A\cap B^c)+P(A\cap B)+P(A^c\cap B)\ .\] Combining all of these equations, we conclude that \[\begin{aligned} P(A)+P(B)-P(A\cap B) &=P(A\cap B)+P(A\cap B^c)+P(A\cap B)+P(A^c\cap B)-P(A\cap B)\\ &= P(A\cap B^c)+P(A\cap B)+P(A^c\cap B) + P(A\cap B)-P(A\cap B)…
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/03%3A_Probability_Topics/3.10%3A_Chapter_ReviewThis page provides an overview of fundamental probability concepts, including terminology, independent and mutually exclusive events, and essential probability rules. It discusses sampling methods and...This page provides an overview of fundamental probability concepts, including terminology, independent and mutually exclusive events, and essential probability rules. It discusses sampling methods and introduces visual tools such as contingency tables, probability trees, and Venn diagrams. These tools assist in organizing data and clarifying relationships between events, enhancing the understanding of intersections, unions, complements, and conditional probabilities.
