If $P(A)=0.45, P(B)=0.25$, and $P(A \mid B)=0.45$, are $A$ and $B$ independent? Yes No Cannot determine

Step 1 ：Given that the probability of event A, denoted as \(P(A)\), is 0.45, the probability of event B, denoted as \(P(B)\), is 0.25, and the conditional probability of A given B, denoted as \(P(A|B)\), is 0.45.

Step 2 ：We know that events A and B are independent if and only if \(P(A \cap B) = P(A)P(B)\).

Step 3 ：We can find \(P(A \cap B)\) using the formula \(P(A \cap B) = P(A|B)P(B)\).

Step 4 ：Substituting the given values into the formula, we get \(P(A \cap B) = 0.45 * 0.25 = 0.1125\).

Step 5 ：We also calculate \(P(A)P(B) = 0.45 * 0.25 = 0.1125\).

Step 6 ：Since \(P(A \cap B)\) equals \(P(A)P(B)\), we can conclude that A and B are independent.

Step 7 ：\(\boxed{\text{Yes, A and B are independent.}}\)