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11.4: Conditional Probability
https://stats.libretexts.org/Courses/Fresno_City_College/New_FCC_DS_21_Finite_Mathematics_-_Spring_2023/11%3A_Probability/11.04%3A_Conditional_Probability
3.2: Terminology
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_Terminology
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 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.
4.2: Conditional Probability
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_Page
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 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}\\ …
3.4: General Multiplication Probability
https://stats.libretexts.org/Courses/Rio_Hondo_College/Math_130%3A_Statistics/03%3A_Probability/3.04%3A_General_Multiplication_Probability
If two events 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 ...If two events 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.
3.2: Probability Terminology
https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/03%3A_Probability_Topics/3.02%3A_Probability_Terminology
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 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.
6.3: Independent Events and Conditional Probabilities
https://stats.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Ikeda)/06%3A_Probability/6.03%3A_Independent_Events_and_Conditional_Probabilities
What do you think the probability is that a man is over six feet tall? If you knew that both his parents were tall would you change your estimate of the probability? A conditional probability is a pro...What do you think the probability is that a man is over six feet tall? If you knew that both his parents were tall would you change your estimate of the probability? A conditional probability is a probability that is based on some prior knowledge.
3.2: Problems on Conditional Probability
https://stats.libretexts.org/Bookshelves/Probability_Theory/Applied_Probability_(Pfeiffer)/03%3A_Conditional_Probability/3.02%3A_Problems_on_Conditional_Probability
Suppose A i is the event the sum of the two digits on a card is $i$ , $0 \le i \le 18$ , and $B_j$ is the event the product of the two digits is $j$ . \(P(A) = P(A|C) P(C) + P(A|C^c) P(C^c) > P(B...Suppose A i is the event the sum of the two digits on a card is $i$ , $0 \le i \le 18$ , and $B_j$ is the event the product of the two digits is $j$ . $P(A) = P(A|C) P(C) + P(A|C^c) P(C^c) > P(B|C) P(C) + P(B|C^c) P(C^c) = P(B)$ . b. $P(A^c|B) > P(A^c)$ iff $P(A^c B) > P(A^c) P(B)$ iff $P(AB) < P(A) P(B)$ iff $P(A|B) < P(A)$ c. $P(A|B) > P(A)$ iff $P(AB) > P(A) P(B)$ iff $P(A^c B^c) > P(A^c) P(B^c)$ iff $P(A^c|B^c) > P(A^c)$
5.3: Conditional Probability Demonstration
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Introductory_Statistics_(Lane)/05%3A_Probability/5.03%3A_Conditional_Probability_Demonstration
The simulation demonstrates how different conditional probabilities would be calculated from the provided data.
3.11: Formula Review
https://stats.libretexts.org/Bookshelves/Applied_Statistics/Business_Statistics_(OpenStax)/03%3A_Probability_Topics/3.11%3A_Formula_Review
This page defines key probability terminology, including events $A$ and $B$ , sample space $S$ , and associated probabilities. It explains independent events (probabilities that multiply) and mutu...This page defines key probability terminology, including events $A$ and $B$ , sample space $S$ , and associated probabilities. It explains independent events (probabilities that multiply) and mutually exclusive events (no overlap). The page also outlines two fundamental rules: the multiplication rule for joint probabilities and the addition rule for the union of events.
11.4: Conditional Probability
https://stats.libretexts.org/Under_Construction/Purgatory/Finite_Mathematics_-_Spring_2023/11%3A_Probability/11.04%3A_Conditional_Probability
We represent conditional probability using a vertical line | that means “if”, or “given that”, or “if we know that”. The event of interest appears on the left of the |. The condition appears on the ri...We represent conditional probability using a vertical line | that means “if”, or “given that”, or “if we know that”. The event of interest appears on the left of the |. The condition appears on the right side of the |. If the condition corresponds to only one row or only one column in the table, then you can ignore the rest of the table and read the conditional probability directly from the row or column indicated by the condition.
5.3: Conditional Probability and Independent Events
https://stats.libretexts.org/Courses/Queensborough_Community_College/MA336%3A_Statistics/05%3A_Basic_Concepts_of_Probability/5.03%3A_Conditional_Probability_and_Independent_Events
A conditional probability is the probability that an event has occurred, taking into account additional information about the result of the experiment. A conditional probability can always be computed...A conditional probability is the probability that an event has occurred, taking into account additional information about the result of the experiment. A conditional probability can always be computed using the formula in the definition. Sometimes it can be computed by discarding part of the sample space. Two events A and B are independent if the probability P(A∩B) of their intersection A ∩ B is equal to the product P(A)⋅P(B) of their individual probabilities.

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