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- https://stats.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/STAT_200%3A_Introductory_Statistics_(OpenStax)_GAYDOS/03%3A_Probability_Topics/3.02%3A_Independent_and_Mutually_Exclusive_EventsTwo events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, ...Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
- https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Book%3A_Introductory_Statistics_(OpenStax)_With_Multimedia_and_Interactivity_LibreTexts_Calculator/03%3A_Probability_Topics/3.02%3A_TerminologyIn this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assig...In this module we learned the basic terminology of probability. The set of all possible outcomes of an experiment is called the sample space. Events are subsets of the sample space, and they are assigned a probability that is a number between zero and one, inclusive.
- https://stats.libretexts.org/Courses/Compton_College/Pre-Statistics/04%3A_Sets/4.02%3A_The_Complement_of_a_SetComplements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in...Complements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in that set. Sometimes it is much easier to find the probability of a complement than of the original set, and there is an easy relationship between the probability of an event happening and the probability of the complement of that event happening.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/21%3A_Math_Review_for_Introductory_Statistics/21.04%3A_Sets/21.4.02%3A_The_Complement_of_a_SetComplements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in...Complements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in that set. Sometimes it is much easier to find the probability of a complement than of the original set, and there is an easy relationship between the probability of an event happening and the probability of the complement of that event happening.
- https://stats.libretexts.org/Courses/Montgomery_College/Support_Course_for_Elementary_Statistics/06%3A_Sets/6.03%3A_The_Complement_of_a_SetComplements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in...Complements come up very often in statistics, so it is worth revisiting this, but instead of graphically we will focus on set notation. Recall that the complement of a set is everything that is not in that set. Sometimes it is much easier to find the probability of a complement than of the original set, and there is an easy relationship between the probability of an event happening and the probability of the complement of that event happening.
- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/03%3A_Probability_Topics/3.02%3A_Probability_TerminologyRemember that \(S\) has six outcomes. \(P(A|B) = \frac{\frac{(\text { the number of outcomes that are } 2 \text { or } 3 \text { and even in } S)}{6}}{\frac{(\text { the number of outcomes that are ev...Remember that \(S\) has six outcomes. \(P(A|B) = \frac{\frac{(\text { the number of outcomes that are } 2 \text { or } 3 \text { and even in } S)}{6}}{\frac{(\text { the number of outcomes that are even in } S)}{6}}=\frac{\frac{1}{6}}{\frac{3}{6}}=\frac{1}{3}\) Odds The odds of an event presents the probability as a ratio of success to failure.
- https://stats.libretexts.org/Courses/City_University_of_New_York/Introductory_Statistics_with_Probability_(CUNY)/04%3A_Probability_Theory/4.03%3A_Conditional_Probability_and_IndependenceTwo events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, ...Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
- https://stats.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/STAT_200%3A_Elementary_Statistics/03%3A_Probability_Topics/3.03%3A_Independent_and_Mutually_Exclusive_EventsTwo events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, ...Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Shafer_and_Zhang)/03%3A_Basic_Concepts_of_Probability/3.02%3A_Complements_Intersections_and_UnionsSome events can be naturally expressed in terms of other, sometimes simpler, events.
- https://stats.libretexts.org/Courses/Rio_Hondo_College/PSY_190%3A_Statistics_for_the_Behavioral_Sciences/04%3A_Basic_Concepts_of_Probability/4.02%3A_Complements_Intersections_and_UnionsSome events can be naturally expressed in terms of other, sometimes simpler, events.
- https://stats.libretexts.org/Courses/Concord_University/Elementary_Statistics/04%3A_Probability_Topics/4.04%3A_Independent_and_Mutually_Exclusive_EventsTwo events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, ...Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. If they are not independent, then they are dependent. In sampling with replacement, with selecting each member with the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member may be chosen only once, and the events are considered not to be independent. When events do not share outcomes, they are mutu
