Question

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).
Event A: The sample contains protein.Event B: The sample contains the protein albumin.
The probability that a sample contains protein and that the protein is albumin is 0.58. Which statement is true?
A.Events A and B are dependent because P(A and B) P(A) + P(B).
B.Events A and B are dependent because P(A and B) = P(A) + P(B).
C.Events A and B are dependent because P(A and B) = P(A)P(B).
D.Events A and B are dependent because P(A and B)     P(A)      P(B).

Answer 1

$Event\ A\ and\ event\ B\ are\ independent\\\\ \ \Leftrightarrow\ \ \ \ P(A\ \cap\ B)=P(A)\ \cdot\ P(B)\\---------------------\\\\P(A)=0.78\ \ \ and\ \ \ P(B)=0.58\ \ \ and\ \ \ P(A\ \cap\ B)=0.58\\\\P(A)\cdot P(B)=0.78\cdot0.58\ \neq \ 0.58\\\\\Rightarrow\ \ \ Event\ A\ and\ event\ B\ are\ dependent\ \ \ \Rightarrow\ \ \ Ans.\ (?)$