in a survey of 1000 fruit eaters who like to eat at least one fruit among apple ,mango amd grapes.400 do not like grape 380 do not like mango and 542 do not like apple, 294 like both mango and apple,277 like both grapes and apple. how many people like exactly one fruit
Answers
Given : Survey of 1000 fruit eaters
400 do not like grape
380 do not like mango
542 do not like apple,
294 like both mango and apple,
277 like both grapes and apple.
120 like both grape and apple
To Find : how many people like exactly one fruit
Solution:
Total = 1000
do not like grape = 400
Like grapes G = 600
do not like mango = 380
Like Mango M = 620
do not like apple = 542
like Apples A = 458
like both mango and apple M ∩ A = 294
like both mango and Grapes M ∩ G = 277
like both apple and Grapes A ∩ G = 120
M ∩ A ∩ G = ?
Total = G + M + A - M ∩ A - M ∩ G - A ∩ G + M ∩ A ∩ G
=> 1000 = 600 + 620 + 458 - 294 - 277 - 120 + M ∩ A ∩ G
=> M ∩ A ∩ G = 13
Likes only grapes = G - M ∩ G - A ∩ G + M ∩ A ∩ G
= 600 - 277 - 120 + 13
= 216
216 people likes only grapes
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