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Recall the condition for independence of two events.

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Step-by-step solution

5 steps
  1. Recall the condition for independence of two events.

    Two events AA and BB are independent if and only if P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B).

  2. Identify the given probabilities.

    We are given:
    P(A)=0.4P(A) = 0.4
    P(B)=0.7P(B) = 0.7
    P(A∩B)=0.28P(A \cap B) = 0.28

  3. Calculate the product P(A)P(B)P(A)P(B).

    P(A)P(B)=(0.4)(0.7)=0.28P(A)P(B) = (0.4)(0.7) = 0.28
  4. Compare P(A∩B)P(A \cap B) with P(A)P(B)P(A)P(B).

    We see that P(A∩B)=0.28P(A \cap B) = 0.28 and P(A)P(B)=0.28P(A)P(B) = 0.28.
    Since P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B), the events AA and BB are independent.

  5. Select the correct option.

    Option A states: "Yes, because P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B)." This matches our finding.

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