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What does partition property mean?
The partition property refers to a principle in mathematics and statistics related to dividing a set or a space into distinct, non-overlapping subsets or partitions, such that the union of these subsets equals the original set. In probability theory, it often pertains to the idea that the probability of an event can be expressed as the sum of the probabilities of mutually exclusive outcomes. This concept is essential for simplifying complex problems and analyzing data by breaking it down into manageable parts.
What is the missing probability P(A)0.35 P(AorB)0.55 P(B)?
To find the missing probability ( P(B) ), you can use the formula for the probability of the union of two events: ( P(A \cup B) = P(A) + P(B) - P(A \cap B) ). Assuming ( P(A \cap B) = 0 ) (which is common unless otherwise specified), you can rearrange the equation: ( P(B) = P(A \cup B) - P(A) = 0.55 - 0.35 = 0.20 ). Thus, ( P(B) = 0.20 ).
How do you find p(b) when p(a) is 23 p(ba) is 12 and p(a U b) is 45 and is a dependent event?
There are symbols missing from your question which I cam struggling to guess and re-insert. p(a) = 2/3 p(b ??? a) = 1/2 p(a ∪ b) = 4/5 p(b) = ? Why use the set notation of Union on the third given probability whereas the second probability has something missing but the "sets" are in the other order, and the order wouldn't matter in sets. There are two possibilities: 1) The second probability is: p(b ∩ a) = p(a ∩ b) = 1/2 → p(a) + p(b) = p(a ∪ b) + p(a ∩ b) → p(b) = p(a ∪ b) + p(a ∩ b) - p(a) = 4/5 + 1/2 - 2/3 = 24/30 + 15/30 - 20/30 = 19/30 2) The second and third probabilities are probabilities of "given that", ie: p(b|a) = 1/2 p(a|b) = 4/5 → Use Bayes theorem: p(b)p(a|b) = p(a)p(b|a) → p(b) = (p(a)p(b|a))/p(a|b) = (2/3 × 1/2) / (4/5) = 2/3 × 1/2 × 5/4 = 5/12
What are Demorgans Law Also explain the use of Demorgans law with example?
The Demorgans Law includes the union, intersection, and complement in mathematics. Examples are A intersection B and B union A. Those are the basic examples.
What does the math word union mean?
ALL the elements in set A combined with all the elements in set B.Example:When A={1,2,3,4} and B={2,3,6} The union of Sets A and B would be: {1,2,3,4,6} , because both sets contain those numbers.
What is principle of additivity?
The principle of additivity states that the probability of the union of two mutually exclusive events is equal to the sum of their individual probabilities. This means that when events are mutually exclusive (cannot both occur at the same time), their probabilities can be added together to find the probability of either event occurring.
What is union probability?
A union probability is denoted by P(X or Y), where X and Y are two events. P(X or Y) is the probability that X will occur or that Y will occur or that both X and Y will occur. The probability of a person wearing glasses or having blond hair is an example of union probability. All people wearing glasses are included in the union, along with all blondes and all blond people who wear glasses. According to Professor Franz Kurfess of California Polytechnic State University, San Luis Obispo, union probability of two independent events A and B can be denoted as: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = P(A) + P(B) - P(A) * P (B)
What does partition property mean?
The partition property refers to a principle in mathematics and statistics related to dividing a set or a space into distinct, non-overlapping subsets or partitions, such that the union of these subsets equals the original set. In probability theory, it often pertains to the idea that the probability of an event can be expressed as the sum of the probabilities of mutually exclusive outcomes. This concept is essential for simplifying complex problems and analyzing data by breaking it down into manageable parts.
What were the differences in ideology and the events that increased tensions between the US and Soviet Union?
Soviet Union was communist.
Assume that A and B are events in a sample spaceWhich of the following could possibly hold:1. P(AUB) < P(A∩B)2. P(AUB) = P(A∩B)3. P(AUB) > P(A∩B) If someone could explain the answer in detail I would appreciate it?
P(A) denotes the probability that event A may occur. 'A' can be a single event or a group of events in which case P(A) is the probability that an event in A may ocur. Thinking just about the events, (AUB) is the union of event A and B, that is the events that are in A and B. (AՈB) is the intersection of A and B, that is the events that are common to A and B. From this you can figure that (AՈB) cannot be larger than (AUB). If A = B, then we have that (AUB) = (AՈB). There is the possibility of (AՈB) being smaller than (AUB) or even being zero if A and B don't have events in common.
What is probability of union and probability of intersection?
probablity of union probabilty of union is define as P(AUB)=P(A)+P(B)-P(AnB) (for not mutualy exclusive data( where atleast one event is common in two samples) P(AUB)=P(A)+P(B) (mutualy exculsive) probablity of intersect P(AnB)=P(A).P(B)
What is the missing probability P(A)0.35 P(AorB)0.55 P(B)?
To find the missing probability ( P(B) ), you can use the formula for the probability of the union of two events: ( P(A \cup B) = P(A) + P(B) - P(A \cap B) ). Assuming ( P(A \cap B) = 0 ) (which is common unless otherwise specified), you can rearrange the equation: ( P(B) = P(A \cup B) - P(A) = 0.55 - 0.35 = 0.20 ). Thus, ( P(B) = 0.20 ).
If forty percent of the workers in a certain factory are members of a union find approximate probability that in a sample of threehundred workers the number of union members is between 100 and 130?
120
What events led to the Bosnian War?
The collapse of the Soviet Union in 1990.
What events officially marked the end of the Soviet Union?
The August Revolt
What events brought on the end of the cold war?
The fall of the Soviet Union
What events in the soviet union led to the end of the cold war?
The Chernobyl disaster Brought about perestroika
