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first prove *: if A intersect B is independent, then A intersect B' is independent. (this is on wiki answers)
P(A' intersect B') = P(B')P(A'|B') by definition
= P(B')[1-P(A|B')] since 1 = P(A) + P(A')
= P(B')[1 - P(A)] from the first proof *
= P(B')P(A') since 1 = P(A) + P(A')
conclude with P(A' intersect B') = P(B')P(A') and is therefore independent by definition.
***note*** i am a student in my first semester of probability so this may be incorrect, but i used the first proof* so i figured i would proof this one to kinda "give back".
What else can I help you with?
What is meant by the union of two or more events?
The union of two or more events refers to a combined outcome that includes all possible outcomes from the events being considered. In probability, the union of events A and B, denoted as A ∪ B, consists of all outcomes that are in either event A, event B, or both. This concept allows us to calculate the likelihood of at least one of the events occurring. For example, if A is rolling a 1 or 2 on a die and B is rolling a 3 or 4, the union A ∪ B includes rolling a 1, 2, 3, or 4.
Why did the 13 colonies want to be independent?
the intolerable acts. no representation in parliament. didnt wanna be involved wit englands wars.
Which events did NOT happen in the 20th century A The War of 1812 B The Spanish-American War C The Great Depression D invention of the first Kodak camera E invention of the cotton gin?
Which events did NOT happen in the 20th century No. A The War of 1812 = 1812, 19th century No. B The Spanish-American War = 1898, 19th century YES. C The Great Depression = 1930s, 20th century No. D invention of the first Kodak camera = first sold 1888, 19th century No. E invention of the cotton gin = patient, 1793, 18th century
Was George B McClellan a Union or Confederate?
George B. McClellan was a Union
What does the ''B'' stand for in Susan B Anthonys name?
Brownell
If A and B are independent events than A and B' are independent?
Yes.
Prove A union B minus A intersection B equals A minus B union B minus A?
complement of c
Is an example of the compliment rule being applied to mutally exclusive events?
Yes, the complement rule can be applied to mutually exclusive events. For example, if you have two mutually exclusive events, A and B, the probability of either event occurring is given by P(A or B) = P(A) + P(B). The complement rule states that the probability of the complement of an event, such as neither A nor B occurring, is 1 minus the probability of A or B, or P(not A and not B) = 1 - P(A or B). Thus, the complement rule effectively helps calculate the probabilities related to mutually exclusive events.
What is the difference between the multiplication rule for independent versus dependent events?
Given two events, A and B, Pr(A and B) = Pr(A)*Pr(B) if A and B are independent and Pr(A and B) = Pr(A | B)*Pr(B) if they are not.
How can the rule for the probability of 2 independent events be extended to 4 or 5 independent events?
p(A and B) = p(A) x p(B) for 2 independent events p(A and B and ...N) = p(A) x p(B) x p(C) x ...x p(N) In words, if these are all independent events, find the individual probabilities if each and multiply them all together.
If A and B are independent events then are A and B' independent?
if P(A)>0 then P(B'|A)=1-P(B|A) so P(A intersect B')=P(A)P(B'|A)=P(A)[1-P(B|A)] =P(A)[1-P(B)] =P(A)P(B') the definition of independent events is if P(A intersect B')=P(A)P(B') that is the proof
Which equation implies that A and B are independent events?
A and B are independent events if the probability of their intersection equals the product of their individual probabilities, which is mathematically expressed as P(A ∩ B) = P(A) * P(B). This means that the occurrence of event A does not affect the occurrence of event B and vice versa. If this equation holds true, then A and B can be considered independent.
Suppose A and B are independent events. If p a 0.3 and what is?
.7
How do you find A complement intersection B complement?
(A' ∩ B') = (A È B)'
What is the occurrence of one event that does not affect the probability of the other?
The occurrence of one event that does not affect the probability of another event is known as independent events. In probability theory, two events A and B are considered independent if the occurrence of A does not influence the occurrence of B, and vice versa. Mathematically, this is expressed as P(A and B) = P(A) × P(B). An example of independent events is flipping a coin and rolling a die; the outcome of the coin does not affect the result of the die roll.
Definition of independent events?
when the occurance of an event B is not affected by the occurance of event A than we can say that these events are not dependent with each other
What is a complement of a subset?
The complement of a subset B within a set A consists of all elements of A which are not in B.
