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?

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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) About Me  (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) About Me  (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.