Urn 1 contains 2 red balls and 3 white balls, Urn 2 contains 1 red ball and 4 white balls, and Urn 3 contains 3 red balls. Urn i is selected with probability proportional to i (for i 1,2,3) and a ball is drawn at random from the selected urn. If the ball is red, what is the probability that the urn it was selected from contains at least one white ball? Define the events and probabilities in your solution precisely, and include a Venn (or Venn-like) diagram of the sample space for this experiment.

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