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IKMC 2017 - Grades 11-12 - Self-study Question 26

IKMC · IKMC 2017 - Grades 11-12 - Self-study

Question 26

Anna has five boxes, as well as five black balls and five white balls. She is allowed to decide how she shares out the balls between the boxes as long as she puts at least one ball into each box. Beate randomly chooses one box and takes one ball without looking. Beate wins if she draws a white ball. Otherwise Anna wins. How should Anna distribute the balls in order to get the highest probability of winning?
  1. One white and one black in each box.
  2. Black balls in three boxes; white balls in the other two.
  3. Black balls in four boxes; all white balls in the fifth.
  4. All white balls in one box, then one black ball in each box.
  5. All black balls in one box, then one white ball in each box.