Unless I'm reading the question wrong P{A $\cup$ B} = P(A) +P(B) - P(A $\cap$ B). Since they have the same probabiliity then P(A) = 0.50, P(B) = 0.50 and P(A $\cap$ B) = 0.25, thus P{A $\cup$ B}= 1-.025=0.75?
Independent events A and B have the same probability p. Find {A U B}
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0Why do they have the same probability? – 2017-01-29
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1Your argument is good, except that the is no reason to assume that $P(A)=0.5$. You're supposed to use the letter $p$ in the answer instead. – 2017-01-29
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2So in that case Unless I'm reading the question wrong P{A $\cup$ B} = P(A) +P(B) - P(A $\cap$ B). Since they have the same probabiliity then P(A) = p, P(B) = p and P(A $\cap$ B) = $p^2$, thus P{A $\cup$ B}= 2p - $p^2$? – 2017-01-29
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1Yup, that's the way to do it. – 2017-01-29
1 Answers
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We assume $P(A)=P(B)=p.$
If $A$ and $B$ are independent, then $$P(A \cap B)=P(A) \cdot P(B)$$ and $$ P(A \cup B)=P(A)+P(B)-P(A \cap B) $$ reads $$ P(A \cup B)=p+p-p \cdot p=2p-p^2. $$