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Example 8: The members of a marching band were asked which musical instruments they play. A total of 23 said that they played trumpet,

Example 8: The members of a marching band were asked which musical instruments they play. A total of 23 said that they played trumpet, 19 said they played drums and 11 said that they played both. There were 46 members who said they played neither trumpet nor drums. What is the probability that a randomly selected member of the band plays either trumpet or drums but not both?

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