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Difficulty:
35%
(medium)
Question Stats:
73% (02:05) correct
27%
(02:38)
wrong
based on 379
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In a recent study, 90 people were surveyed about what type of animal they owned as a pet. Everyone surveyed owned at least one animal. The results are shown in the Venn diagram. Approximately what percent of the respondents said they had a dog and a cat but no birds?
A. 15%
B. 17%
C. 30%
D. 46%
E. 90%
Attachment:
set217.jpg [ 28.47 KiB | Viewed 7603 times ]
03 Jul 2018, 13:13
Kudos
Bookmarks
Bunuel
Number having both dog and cat and not birds is given by GREEN portion and sum of all portions is 90..
29+4+2+17+9+14+G=90....G=90-75=15
%=100*15/90=50/3=~17%
B
03 Jul 2018, 13:14
Kudos
Bookmarks
From the question stem, we can deduce that P(Total) = 90 and P(Neither) = 0
Given data:
P(Only Dogs) = 29 | P(Only Cats) = 17 | P(Only Birds) = 14 | P(All 3) = 2 | P(Birds U Cats) = 9 | P(Birds U Dogs) = 4
Let's assume P(Dogs U Cats) to be x
P(Total) = P(Only Dogs) + P(Only Cats) + P(Only Birds) + P(Birds U Cats) + P(Birds U Dogs) + P(Dogs U Cats) + P(Neither)
Substituting the values given, we get \(90 = 29 + 17 + 14 + 9 + 4 + x + 2\)-> \(x = 90 - 75 = 15\)
Therefore, the percentage of the respondents who had a dog & a cat but no birds is \(\frac{15}{90}*100 = \frac{50}{3}\) = approximately 17%(Option B)
