In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?

Expert Solution

In a group of 20 musicians, 12 play piano, 7 play trumpet and 2 play both piano and trumpet.

Consider the Addition Principle,

“If one event can occur in m ways and a second event with no common outcomes can occur in n ways, then first or second event can occur in m + n ways.”

Two musicians play both piano and trumpet. Hence, 2 will be subtracted from the sum of number of musicians who play piano and the number of musicians who play trumpet.

That is, the number of musicians who play either piano or trumpet will be equal to the “number of musicians who play piano” plus “number of musicians who play trumpet” minus 2.

12 + 7 – 2 = 17

Therefore, the number of musicians who play either piano or trumpet will be 17.

Junaid answered 1 year ago

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