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3.3: Independent and Mutually Exclusive Events
https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/03%3A_Probability_Topics/3.03%3A_Independent_and_Mutually_Exclusive_Events
Independent Events Two events are independent if one of the following are true: Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. The o...Independent Events Two events are independent if one of the following are true: Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. The outcome of the first roll does not change the probability for the outcome of the second roll. If it is not known whether A and B are independent or dependent, assume they are dependent until you can show otherwise. Are $T$ and $F$ independent?. Are $F$ and $S$ mutually exclusive?
3.3: Two Basic Rules of Probability
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_Probability
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...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.
3.4: Two Basic Rules of Probability
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_Probability
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 ...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.
3.3: Independent and Mutually Exclusive Events
https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/03%3A_Probability_Topics/3.03%3A_Independent_and_Mutually_Exclusive_Events
Independent Events Two events are independent if one of the following are true: Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. The o...Independent Events Two events are independent if one of the following are true: Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. The outcome of the first roll does not change the probability for the outcome of the second roll. If it is not known whether A and B are independent or dependent, assume they are dependent until you can show otherwise. Are $T$ and $F$ independent?. Are $F$ and $S$ mutually exclusive?
3.3: Two Basic Rules of Probability
https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/03%3A_Probability_Topics/3.03%3A_Two_Basic_Rules_of_Probability
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 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.
3.4: Two Basic Rules of Probability
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_Probability
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 ...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.

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