I am studying for the p exam and realized I really need to brush up on my basic set theory, and am having trouble with this question. In a survey on Popsicle flavor preferences of kids aged 3-5, it was found that: • 22 like strawberry.• 25 like blueberry.• 39 like grape.• 9 like blueberry and strawberry.• 17 like strawberry and grape.• 20 like blueberry and grape.• 6 like all flavors.• 4 like none. Apparently the answer is 50, but I can't seem to figure out how to arrive at this

aurelegena 2022-10-02 Answered
I am studying for the p exam and realized I really need to brush up on my basic set theory, and am having trouble with this question.
In a survey on Popsicle flavor preferences of kids aged 3-5, it was found that:
- 22 like strawberry.
- 25 like blueberry.
- 39 like grape.
- 9 like blueberry and strawberry.
- 17 like strawberry and grape.
- 20 like blueberry and grape.
- 6 like all flavors.
- 4 like none.
Apparently the answer is 50, but I can't seem to figure out how to arrive at this
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Answers (1)

Radman76
Answered 2022-10-03 Author has 7 answers
Note that
P ( A B C ) = P ( A ) + P ( B ) + P ( C ) P ( A B ) P ( A C ) P ( B C ) + P ( A B C ) .
Now let A be "kid likes strawberry", B be "kid likes blueberry", C be "kid likes grape", and n be the number of kids.
P(A)=22/n, P(B)=25/n, P(C)=39/n, with intersections 9/n, 17/n, 20/n, 6/n.
Then the probability of liking any flavor at all is
P ( A B C ) = ( 22 + 25 + 39 9 17 20 + 6 ) / n = 46 / n .
Also, the probability of not liking any flavor at all is 4/n, but also
4 / n = P ( A c B c C c ) = 1 P ( A B C ) = 1 46 / n .
Therefore,
4 n = 1 46 n = n 46 n ,
so 4=n−46, and so n=50.
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