Picking a box then a ball

Suppose that there are two boxes, labeled odd and even. The odd box contains three balls numbered 1,3,5 and the even box contains two balls labeled 2,4. One of the boxes is picked randomly by tossing a fair coin.

  1. What is the probability that a 3 is chosen ?
  2. What is the probability a number less than or equal to 2 is chosen ?
  3. The above procedure produces a distribution on \(\{1,2,3,4,5\}\) how does it compare to picking a number uniformly (with equal probability) ?




[Pitman p 37, example 5]

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