Recall the condition for independence of two events.
This history question requires analysis of historical events, causes, and consequences. The detailed answer below provides context, evidence, and a well-structured explanation.
ScanSolve AI Answer
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Step 1: Recall the condition for independence of two events.
Two events $A$ and $B$ are independent if and only if $P(A \cap B) = P(A)P(B)$.
Step 2: Identify the given probabilities.
We are given:
$P(A) = 0.4$
$P(B) = 0.7$
$P(A \cap B) = 0.28$
Step 3: Calculate the product $P(A)P(B)$.
$$P(A)P(B) = (0.4)(0.7) = 0.28$$
Step 4: Compare $P(A \cap B)$ with $P(A)P(B)$.
We see that $P(A \cap B) = 0.28$ and $P(A)P(B) = 0.28$.
Since $P(A \cap B) = P(A)P(B)$, the events $A$ and $B$ are independent.
Step 5: Select the correct option.
Option A states: "Yes, because $P(A \cap B) = P(A)P(B)$." This matches our finding.
The final answer is $\boxed{\text{A}}$
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