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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.

4.3: Working with Events

https://math.libretexts.org/Courses/Rio_Hondo/Math_150%3A_Survey_of_Mathematics/04%3A_Probability/4.03%3A_Working_with_Events

where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurri...where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.

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

9.3: Working with Events

https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/09%3A_Probability/9.03%3A_Working_with_Events

where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurri...where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.

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.

8.2: Mutually Exclusive Events and the Addition Rule

https://math.libretexts.org/Courses/Community_College_of_Denver/MAT_1320_Finite_Mathematics_2e/08%3A_Probability/8.02%3A_Mutually_Exclusive_Events_and_the_Addition_Rule

Given two events, E, F, then finding the probability of E

$\cup$ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the numb...Given two events, E, F, then finding the probability of E

$\cup$ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the number shown on the die is an even number, and let F be the event that the number shown is greater than four. If we count the number of elements n(E) in E, and add to it the number of elements n(F) in F, the points in both E and F are counted twice, once as elements of E and once as elements of F.

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.

3.6: Working with Events

https://math.libretexts.org/Courses/Cerritos_College/Mathematics_for_Technology/03%3A_Module_3-_Probability_and_Statistics/3.06%3A_Working_with_Events

where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurri...where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.

6.2: Probability Rules with "Not," "Or" and "And"

https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/06%3A_Probability/6.02%3A_Probability_Rules_with_Not_Or_and_And

The complement of event

$A$ is the event “

$A$ does not happen.” It is the set of outcomes in the sample space

$S$ that are not in event

$A$ . Say we look at the event of drawing a single card f...The complement of event

$A$ is the event “

$A$ does not happen.” It is the set of outcomes in the sample space

$S$ that are not in event

$A$ . Say we look at the event of drawing a single card from a deck and the outcome of drawing a "red card or a jack". If you count the number of options for red cards and the number of options for a jack, you are counting the red jacks twice.

7.2: Mutually Exclusive Events and the Addition Rule

https://math.libretexts.org/Courses/Los_Angeles_City_College/Math_230-Mathematics_for_Liberal_Arts_Students/07%3A_Probability/7.02%3A_Mutually_Exclusive_Events_and_the_Addition_Rule

Given two events, E, F, then finding the probability of E

$\cup$ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the numb...Given two events, E, F, then finding the probability of E

$\cup$ F, is the same as finding the probability that E will happen, or F will happen, or both will happen. Let E be the event that the number shown on the die is an even number, and let F be the event that the number shown is greater than four. If we count the number of elements n(E) in E, and add to it the number of elements n(F) in F, the points in both E and F are counted twice, once as elements of E and once as elements of F.

3.3: Working with Events

https://math.libretexts.org/Courses/Northwest_Florida_State_College/MGF_1131%3A_Mathematics_in_Context/03%3A_Probability/3.03%3A_Working_with_Events

where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurri...where

$P(A \text { and } B)$ is the probability of events

$A$ and

$B$ both occurring,

$P(A)$ is the probability of event

$A$ occurring, and

$P(B)$ is the probability of event

$B$ occurring If you look back at the coin and die example from earlier, you can see how the number of outcomes of the first event multiplied by the number of outcomes in the second event multiplied to equal the total number of possible outcomes in the combined event.

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