Question

help please!!!!
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?

Answer 1

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).

Answer 2

\[P(A)=0.73\]\[P(B)=0.58\]\[P(A|B)=1\]
Condition for independent events:
\[P(AintersectionB)=P(A) \times P(B)\]
and from conditional probability we have\[P(A|B)=\frac{P(AintersectionB)}{P(B)}\]\[\implies P(AintersectionB)=P(A|B) \times P(B)=1 \times 0.58=0.58\]
Further we calculate \[P(A) \times P(B)=0.73 \times 0.58=0.4234\]
Anything you can observe from these calculations?