Problem

Events $A$ and $B$ are independent with $p(A)=0.6$ and $p(B)=0.8$. Find $p(A \cup B)$.

Answer

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Answer

Final Answer: The probability of the union of events A and B is \(\boxed{0.92}\)

Steps

Step 1 ：Given that events A and B are independent with probabilities p(A)=0.6 and p(B)=0.8 respectively.

Step 2 ：The probability of the union of two independent events A and B is given by the formula: \(p(A \cup B) = p(A) + p(B) - p(A) \cdot p(B)\)

Step 3 ：Substitute the given probabilities into this formula: \(p(A \cup B) = 0.6 + 0.8 - 0.6 \cdot 0.8\)

Step 4 ：Simplify to get the final answer: \(p(A \cup B) = 0.92\)

Step 5 ：Final Answer: The probability of the union of events A and B is \(\boxed{0.92}\)

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