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- https://stats.libretexts.org/Courses/Concord_University/Elementary_Statistics/04%3A_Probability_Topics/4.05%3A_Two_Basic_Rules_of_ProbabilityThe multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has t...The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has 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 not independent. The events A and B are mutually exclusive events when they have no common outcomes.
- 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/3.04%3A_Two_Basic_Rules_of_ProbabilityThe multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has t...The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has 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 not independent. The events A and B are mutually exclusive events when they have no common outcomes.
- https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Book%3A_Introductory_Statistics_(OpenStax)_With_Multimedia_and_Interactivity/11%3A_The_Chi-Square_Distribution/11.04%3A_Test_of_IndependenceTests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test.
- https://stats.libretexts.org/Courses/Long_Beach_City_College/Book%3A_STAT_227_-_Introductory_Statistics/Text/11%3A_The_Chi-Square_Distribution/11.04%3A_Test_of_IndependenceTests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test.
- 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/4.02%3A_New_PageBut the first roll having any particular value is independent of the second roll having another, e.g., if A={11,12,13,14,15,16} is the event in that sample space of getting a 1 on the f...But the first roll having any particular value is independent of the second roll having another, e.g., if A={11,12,13,14,15,16} is the event in that sample space of getting a 1 on the first roll and B={14,24,34,44,54,64} is the event of getting a 4 on the second roll, then events A and B are independent, as we check by using Fact 4.2.5: \[\begin{aligned} P(A\cap B) &= P(\{14\})\\ &= \frac{1}{36}\\ &= \frac16\cdot\frac16\\ &= \frac{6}{36}\cdot\frac{6}{36}\\ …
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_1e_(OpenStax)/11%3A_The_Chi-Square_Distribution/11.04%3A_Test_of_IndependenceTests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_1e_(OpenStax)/03%3A_Probability_Topics/3.04%3A_Two_Basic_Rules_of_ProbabilityThe multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has t...The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has 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 not independent. The events A and B are mutually exclusive events when they have no common outcomes.
- https://stats.libretexts.org/Courses/Compton_College/Pre-Statistics/10%3A_Probability_Topics/10.04%3A_Two_Basic_Rules_of_ProbabilityThe multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has t...The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has 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 not independent. The events A and B are mutually exclusive events when they have no common outcomes.
- https://stats.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/STAT_200%3A_Introductory_Statistics_(OpenStax)_GAYDOS/03%3A_Probability_Topics/3.03%3A_Two_Basic_Rules_of_ProbabilityThe multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has t...The multiplication rule and the addition rule are used for computing the probability of A and B, and the probability of A or B for two given events A, B. In sampling with replacement each member has 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 not independent. The events A and B are mutually exclusive events when they have no common outcomes.
- https://stats.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/STAT_200%3A_Introductory_Statistics_(OpenStax)_GAYDOS/11%3A_The_Chi-Square_Distribution/11.03%3A_Test_of_IndependenceTests of independence involve using a contingency table of observed (data) values. The test statistic for a test of independence is similar to that of a goodness-of-fit test.
