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Which pairs of events are independent? (a) P(A) = 0.29, P(B) = 0.52, P(A∩B) = 0.12. (b) P(A) = 0.31, P(B) = 0.21, P(A∩B) = 0.05. (c) P(A) = 0.80, P(B) = 0.30, P(A∩B) = 0.30.

Respuesta :

Answer:  None

Step-by-step explanation:

Two events are independent if and only if P(A ∩ B) = P(A)*P(B).

  • Let's look at choice (a). P(A)*P(B) = 0.29*0.52 = 0.1508 which does not match with P(A∩B) = 0.12, so we can rule out choice (a).
  • Now onto choice (b). P(A)*P(B) = 0.31*0.21= 0.1508 which does not match with P(A∩B) = 0.0651, so we can rule out choice (b).
  • Lastly choice (c). P(A)*P(B) = 0.80*0.30 = 0.24 which does not match with P(A∩B) = 0.30, so we rule this out as well.

Unfortunately none of the given choices represent independent events.

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