The probability that a given urine sample analyzed in a pathology lab contains protein is 0.73 (event A). The probability that the urine sample contains the protein albumin is 0.58 (event B). The probability that a sample contains protein, given that albumin is detected, is 1.
Which statement is true?

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Events A and B are dependent because P(A|B) = P(A).
Events A and B are dependent because P(A| B) P(B).
Events A and B are dependent because P(A|B) = P(A) + P(B).
Events A and B are dependent because P(A| B) P(A).
Events A and B are dependent because P(A|B) = P(A).

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@linn99123 @mathmate please help

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- mathmate

@Kitty449
These are "definition" type of questions which verifies the understanding of given terms, such as "conditional probability" and "dependence" in this case.
The first step in solving this type of problems is to find out the meaning of each term.
For example,
P(A) represents the probability of event A occurring, and similarly,
P(B) represents the probability of event B occurring, and similarly,
P(A|B) represents the probability of event A happening given that B has already occurred.
(you should reread the question to find out what the value of P(A|B) is, for this problem.
It reads "Probability of A given B".
Then you need to know what constitutes dependence.
If you google for the term (in statistics), you will find the following or similar definitions:
(from thefreedictionary.com)
statistical dependence
1. (Statistics) a condition in which two random variables are not independent. X and Y are positively dependent if the conditional probability, P(X|Y), of X given Y is greater than the probability, P(X), of X, or equivalently if P(X&Y) >P(X).P(Y). They are negatively dependent if the inequalities are reversed.
In other words, if P(X|Y)\(\ne\)P(X), then X and Y are dependent.
In fact, the definition of statistical independence between X and Y if and only if P(X|Y)=P(X), which says the same thing.
So look at the values of P(A), P(B), and P(A|B), then you can decide why A and B are dependent (or not).
Btw, your 5 choices are incomplete, but we don't need it more than you do.
It is a normal courtesy to proof-read your post and correct as required before your helpers work on it.

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