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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.
What else can I help you with?
If A and B are independent events than A and B' are independent?
Yes.
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.
What is the slope intercept form of the equation for the line that passes through the point (-10-6) and has a slope of -1?
The slope-intercept form of a line is given by the equation ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Given a slope ( m = -1 ) and a point (-10, -6), we can substitute these values into the equation to find ( b ): [ -6 = -1(-10) + b \implies -6 = 10 + b \implies b = -16. ] Thus, the slope-intercept form of the line is ( y = -x - 16 ).
What does the equation for a linear relationship stand for?
y=mx+b is the equation for a linear relationship. y= the dependant variable m= the slope of the line x= the independent variable b= the y-intercept
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.
If A and B are independent events than A and B' are independent?
Yes.
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
What is the slope intercept form of the equation for the line that passes through the point (-10-6) and has a slope of -1?
The slope-intercept form of a line is given by the equation ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Given a slope ( m = -1 ) and a point (-10, -6), we can substitute these values into the equation to find ( b ): [ -6 = -1(-10) + b \implies -6 = 10 + b \implies b = -16. ] Thus, the slope-intercept form of the line is ( y = -x - 16 ).
What does the equation for a linear relationship stand for?
y=mx+b is the equation for a linear relationship. y= the dependant variable m= the slope of the line x= the independent variable b= the y-intercept
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
When two probabilities are multiplied is this a compound event?
Yes, when two probabilities are multiplied, it typically indicates a compound event, specifically in the context of independent events. This multiplication reflects the likelihood of both events occurring together. For instance, if you have two independent events A and B, the probability of both occurring is calculated by multiplying their individual probabilities: P(A and B) = P(A) × P(B). However, if the events are not independent, you would need to consider their relationship to determine the combined probability correctly.
How do you draw a Venn diagram to the probability of two independent events a and b?
the circles do not overlap at all.
Prove that the complement of A and B are independent events?
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".
