TU Wien:Statistik und Wahrscheinlichkeitstheorie UE (Bura)/Übungen 2019W/1.3: Unterschied zwischen den Versionen

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;Independence
 
;Independence
 
Let A and B be independent events.
 
Let A and B be independent events.
:(a) Prove that A c and B c are also independent.
+
:(a) Prove that <math>A^c</math> and <math>B^c</math> are also independent.
 
:(b) If we additionally know that <math>P(A|B) = 0.6</math> and <math>P(B|A) = 0.3</math>, compute the probabilities of the following events
 
:(b) If we additionally know that <math>P(A|B) = 0.6</math> and <math>P(B|A) = 0.3</math>, compute the probabilities of the following events
 
::(i) at most one of A or B
 
::(i) at most one of A or B

Version vom 12. Oktober 2019, 19:30 Uhr

Independence

Let A and B be independent events.

(a) Prove that A^c and B^c are also independent.
(b) If we additionally know that P(A|B) = 0.6 and P(B|A) = 0.3, compute the probabilities of the following events
(i) at most one of A or B
(ii) either A or B but not both.

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