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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?
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
1889 Susan B Anthony B silver dollar worth?
100
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
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
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)'
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.
How do you find A complement given B complement?
P(A given B')=[P(A)-P(AnB)]/[1-P(B)].
How do you draw a Venn diagram to the probability of two independent events a and b?
the circles do not overlap at all.
What is mutual complement?
Mutual complement refers to two sets or events that, when combined, cover the entire sample space without any overlap. In probability and set theory, if two events A and B are mutual complements, then the occurrence of one event means the other cannot occur; mathematically, this is expressed as A ∩ B' = 0 and A ∪ B = S, where S is the sample space. Essentially, they are opposites that together account for all possible outcomes.
