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A ball is drawn at random from an urn containing one red and one white ball. If the white ball is drawn, it is put

A ball is drawn at random from an urn containing one red and one white ball. If the white ball is drawn, it is put back into the urn. If the red ball is drawn, it is returned to the urn together with two more red balls. Then a second draw is made.

  1. What is the probability a red ball was drawn on both the first and the second draws?
  2. What is the probability that the second draw is W?
  3. If the second draw was Red, what is the probability that the first draw was Red too?

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