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Math Help - Probability - A box of chocolates with nuts

  1. #1
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    Probability - A box of chocolates with nuts

    I'm doing some review and I'm stuck on the following question.

    John owns a chocolate shop. His most popular item is a box of 40 assorted chocolates, 5 of which contain nuts. Due to the popularity of chocolates with nuts, he plans to double the number of them in each box. He claims that having 10 of the 40 chocolates contain nuts will double the probability that one or both of two randomly selected chocolates will contain nuts. Do you agree? Use combinatorial probability and the probability product rule to support your answer.
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    Compare  \frac {\binom {5}{1} \binom {35}{1}  + \binom {5}{2}} {\binom {40}{2}} with  \frac {\binom {10}{1} \binom {30}{1}  + \binom {10}{2}} {\binom {40}{2}}.
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