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probability that a player's pick wins the grand prize

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In a certain lottery, k balls are chosen at random and without replacement from a bin containing N balls numbered 1 through N. A player picks k + 2 numbers between 1 and N. The player wins the grand prize if their pick contains all k of the lottery numbers.
(a) Set up a probability space to model this experiment.
(b) Find the probability that a player's pick wins the grand prize.

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The solution finds the probability that a player's pick wins the grand prize.

Solution provided by:
  • BSc, University of Bucharest
  • MSc, Ovidius
  • MSc, Stony Brook
  • PhD (IP), Stony Brook
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