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n coins are given, among which exactly 3 are bad and heavier than the good ones. A balance is used to identify the bad coins. Assume k coins are picked in both sides of the balance at a time. What is the probability of

  1. left side being heavier
  2. right side being heavier
  3. both sides being equal in weight

Thanks.

  • 3
    Can you make any progress on the problem? Do you know how many ways there are to choose two sets of $k$ coins each from a total of $n$ coins? It's easier to pitch an answer to your level, if people know what that level is.2012-05-11
  • 0
    There are three bad coins. Sorry for the confusion.2012-05-11
  • 1
    2kCn is the number of ways to choose n coins from 2k coins. Since both sides must have an equal (k) number of coins, it's slightly more complicated. It might help to think about first choosing $k$ coins for the left side, and then choosing $k$ coins for the right side, taking into account that for the right side, you have $n-k$ coins to choose from.2012-05-11

4 Answers 4