jiz Me: 12.1-1 Find probabilities and odds involving compound events.
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Frank Berguin 9 | 08/02/25 9:23 AM
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The probabilities of events \( \mathrm{A}, \mathrm{B} \), and \( \mathrm{A} \cap \mathrm{B} \) are given. Find (a) \( \mathrm{P}(\mathrm{A} \cup \mathrm{B}) \), (b) the odds in favor of and the odds against A , (c) the odds in favor of and the odds against \( B \), and (d) the odds in favor of and against \( A \cap B \).
\[
P(A)=\frac{2}{7}, P(B)=\frac{4}{7}, P(A \cap B)=\frac{1}{7}
\]
(a) \( P(A \cup B)= \) \( \square \) (Simplify your answer.)
(b) The odds in favor of A are \( \square \) : \( \square \) .
(Simplify your answer. Type whole numbers.)
The odds against \( A \) are \( \square \) : \( \square \) .
(Simplify your answer. Type whole numbers.)
(c) The odds in favor of B are \( \square \) : \( \square \) .
(Simplify your answer. Type whole numbers.)
The odds against B are \( \square \) : \( \square \) .
(Simplify your answer. Type whole numbers.)
(d) The odds in favor of \( A \cap B \) are \( \square \) : \( \square \) .
(Simplify your answer. Type whole numbers.)
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