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4.4: Two Basic Rules of Probability
https://math.libretexts.org/Courses/Coastline_College/Math_C160%3A_Introduction_to_Statistics_(Tran)/04%3A_Probability_Topics/4.04%3A_Two_Basic_Rules_of_Probability
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 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.
12.2: Test of Independence
https://math.libretexts.org/Courses/Heartland_Community_College/HCC%3A_Introduction_to_Statistics_(Lathrop)/12%3A_Categorical_Data/12.2%3A_Test_of_Independence
Tests 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.
12.4: Test of Independence
https://math.libretexts.org/Courses/Coastline_College/Math_C160%3A_Introduction_to_Statistics_(Tran)/12%3A_The_Chi-Square_Distribution/12.04%3A_Test_of_Independence
Tests 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.
11.3: Test of Independence
https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Sklar)/11%3A_The_Chi-Square_Distribution/11.03%3A_Test_of_Independence
Tests 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.
3.3: Independent and Mutually Exclusive Events
https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Kravets)/03%3A_Probability_Topics/3.03%3A_Independent_and_Mutually_Exclusive_Events
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, ...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
6.6: Independent Events
https://math.libretexts.org/Under_Construction/Purgatory/MAT_1320_Finite_Mathematics/06%3A_Probability/6.6%3A_Independent_Events
$P$ (The card is a king | The card is a face card) $\neq$ $P$ (The card is a king) In other words, the additional information, knowing that the card selected is a face card changed the probability... $P$ (The card is a king | The card is a face card) $\neq$ $P$ (The card is a king) In other words, the additional information, knowing that the card selected is a face card changed the probability of obtaining a king. $P$ (The card is a king | A red card has shown) = $P$ (The card is a king) Whenever the probability of an event $E$ is not affected by the occurrence of another event $F$ , and vice versa, we say that the two events $E$ and $F$ are independent.
5.4: Test of Independence
https://math.libretexts.org/Courses/Austin_Peay_State_University/Supplementary_Material_for_Math_Models/05%3A_The_Chi-Square_Distribution/5.04%3A_Test_of_Independence
Tests 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.
7.5: Independent Events
https://math.libretexts.org/Courses/Los_Angeles_City_College/Math_230-Mathematics_for_Liberal_Arts_Students/07%3A_Probability/7.05%3A_Independent_Events
$P$ (The card is a king | The card is a face card) $\neq$ $P$ (The card is a king) Whenever the probability of an event $E$ is not affected by the occurrence of another event $F$ , and vice ver... $P$ (The card is a king | The card is a face card) $\neq$ $P$ (The card is a king) Whenever the probability of an event $E$ is not affected by the occurrence of another event $F$ , and vice versa, we say that the two events $E$ and $F$ are independent. Both solutions to Example $\PageIndex{8}$ are actually the same, except that in Solution 2 we delayed substituting the values into the equation until after we solved the equation for $P(A \cap B)$ .
12.4: Test of Independence
https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Kravets)/12%3A_The_Chi-Square_Distribution_and_Chi-Square_Tests/12.04%3A_Test_of_Independence
Tests 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.
9.4: Two Basic Rules of Probability
https://math.libretexts.org/Courses/Coalinga_College/Math_for_Educators_(MATH_010A_and_010B_CID120)/09%3A_Probability_Topics/9.04%3A_Two_Basic_Rules_of_Probability
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 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.
3.3: Two Basic Rules of Probability
https://math.libretexts.org/Courses/Mission_College/Math_10%3A_Elementary_Statistics_(Sklar)/03%3A_Probability_Topics/3.03%3A_Two_Basic_Rules_of_Probability
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 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.

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