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- https://stats.libretexts.org/Courses/Las_Positas_College/Math_40%3A_Statistics_and_Probability/04%3A_Probability_and_Counting/4.05%3A_Probability_And_Counting_RulesFor the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. Th...For the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. There are 365 possible choices for the first person and since the second person must have a different birthday, there are 364 choices for the second, 363 for the third, and so on.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/03%3A_Probability_Topics/3.11%3A_Formula_ReviewThis page defines key probability terminology, including events A and B, sample space S, and associated probabilities. It explains independent events (probabilities that multiply) and mutu...This page defines key probability terminology, including events A and B, sample space S, and associated probabilities. It explains independent events (probabilities that multiply) and mutually exclusive events (no overlap). The page also outlines two fundamental rules: the multiplication rule for joint probabilities and the addition rule for the union of events.
- https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/BFE_1201_Statistical_Methods_for_Finance_(Kuter)/03%3A_Probability_Topics/3.03%3A_Two_Basic_Rules_of_ProbabilityThis equation is read as the probability of A given B equals the probability of A and B divided by the probability of B. Then P(A\cap B)=P(A|B)P(B) becomes P(A\cap B)=P(A)(B) because the \(P(A...This equation is read as the probability of A given B equals the probability of A and B divided by the probability of B. Then P(A\cap B)=P(A|B)P(B) becomes P(A\cap B)=P(A)(B) because the P(A|B)=P(A) if A and B are independent. We can think of the union symbol substituting for the word "or". The reason we subtract the intersection of A and B is to keep from double counting elements that are in both A and B.
- https://stats.libretexts.org/Under_Construction/Purgatory/FCC_-_Finite_Mathematics_-_Spring_2023/11%3A_Probability/11.03%3A_Probability_Using_Tree_Diagrams_and_CombinationsFor the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. Th...For the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. There are 365 possible choices for the first person and since the second person must have a different birthday, there are 364 choices for the second, 363 for the third, and so on.
- https://stats.libretexts.org/Sandboxes/JolieGreen/Finite_Mathematics_-_Spring_2023_-_OER/11%3A_Probability/11.03%3A_Probability_Using_Tree_Diagrams_and_CombinationsFor the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. Th...For the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. There are 365 possible choices for the first person and since the second person must have a different birthday, there are 364 choices for the second, 363 for the third, and so on.
- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/03%3A_Probability_Topics/3.04%3A_Two_Basic_Rules_of_ProbabilityWe can think of the intersection symbol as substituting for the word "and". This rule may also be written as: P(A | B)=\frac{P(A \cap B)}{P(B)} This equation is read as the probability of A given ...We can think of the intersection symbol as substituting for the word "and". This rule may also be written as: P(A | B)=\frac{P(A \cap B)}{P(B)} This equation is read as the probability of A given B equals the probability of A and B divided by the probability of B. We can think of the union symbol substituting for the word "or". The reason we subtract the intersection of A and B is to keep from double counting elements that are in both A and B.
- https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/11%3A_Probability/11.03%3A_Probability_Using_Tree_Diagrams_and_CombinationsFor the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. Th...For the probability that one marble is red and the other is white, we observe that this can be satisfied if the first is red and the second is white, or if the first is white and the second is red. There are 365 possible choices for the first person and since the second person must have a different birthday, there are 364 choices for the second, 363 for the third, and so on.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/03%3A_Probability_Topics/3.03%3A_Two_Basic_Rules_of_ProbabilityThis page explains two key probability rules: the Multiplication Rule, which calculates the probability of two events happening together, and the Addition Rule, which assesses the chances of either ev...This page explains two key probability rules: the Multiplication Rule, which calculates the probability of two events happening together, and the Addition Rule, which assesses the chances of either event happening while considering overlaps. It notes that the multiplication rule simplifies for independent events, while the addition rule applies differently to mutually exclusive events. An example involving a student's library activities illustrates these concepts in practice.
- https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/03%3A_Probability_Topics/3.04%3A_Two_Basic_Rules_of_ProbabilityWe can think of the intersection symbol as substituting for the word "and". This rule may also be written as: P(A | B)=\frac{P(A \cap B)}{P(B)} This equation is read as the probability of A given ...We can think of the intersection symbol as substituting for the word "and". This rule may also be written as: P(A | B)=\frac{P(A \cap B)}{P(B)} This equation is read as the probability of A given B equals the probability of A and B divided by the probability of B. We can think of the union symbol substituting for the word "or". The reason we subtract the intersection of A and B is to keep from double counting elements that are in both A and B.
- https://stats.libretexts.org/Courses/Fresno_City_College/New_FCC_DS_21_Finite_Mathematics_-_Spring_2023/11%3A_Probability/11.03%3A_Probability_Using_Tree_Diagrams_and_Combinations
- https://stats.libretexts.org/Courses/Rio_Hondo_College/Math_130%3A_Statistics/03%3A_Probability/3.03%3A_Multiplication_Rule_for_Independent_EventsTwo events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs.
