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Prove that if A and B are independent events, then A' and B' must also be independent.

Question:

Prove that if A and B are independent events, then A' and B' must also be independent.

Complementary Events:

When two events are said to be complementary, then the sum of their probabilities must be {eq}1 {/eq} and the one event is exactly the opposite of the other event.

Answer and Explanation:

When {eq}A {/eq} and {eq}B {/eq} are two independent events.

{eq}P(A \cap B) = P(A)\cdot P(B) {/eq}


{eq}\begin{align*} P(A^c \cap B^c) & = 1 -...

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Probability of Simple, Compound and Complementary Events

from Math 102: College Mathematics

Chapter 13 / Lesson 5
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