SOLUTION: In a group of 250 music lovers 135 like folk songs and 150 like modern songs find 1) how many like both the songs? 2) how many like only one songs?

Question 1083104: In a group of 250 music lovers 135 like folk songs and 150 like modern songs find 1) how many like both the songs? 2) how many like only one songs?
Found 2 solutions by Boreal, natolino_2017:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
P( A or B)=P(A)+P(B)-P(BOTH)
250=135+150-P(BOTH)
P(BOTH)=35
P(ONE)=215
Answer by natolino_2017(77) (Show Source): You can put this solution on YOUR website!
Let A: Folk Songs.
B: Modern Song.
i) #(AorB) = 250 (Universe)
ii) 135 = #(justA) + #(AandB)
iii) 150 = #(justB) + #(AandB)
ii) +iii) 285 = #(justA) + 2*(#(AandB)) + #(justB)
with i) 285 =(#(justA) + (#(AandB)) + #(justB)) + (#(AandB))
285 = 250 + #(AandB)
#(AandB) = 35.
So 1) 35 like both the song.
2) (#JustA) = 135 - 35 = 100.
(#JustB) = 150 - 35 = 115.
So 100 +115 = 215 like only one song.
@natolino.

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