Fruit Lovers

Probability Level 2

You're interviewing 100 subjects about their favorite fruits (apples, bananas, and oranges), and the number of fruit lovers are classified in the table above. For example, from the data, there are 63 apple lovers (with or without other fruits), and 24 people love bananas and oranges (with or without apples).

If everyone loves at least one kind of fruit, how many people love all 3 kinds of fruits?


The answer is 10.

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Worranat Pakornrat by Worranat Pakornrat , 36, Thailand

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1 solution

Let A A be the set of apple lovers, B B be the set of banana lovers, and C C be the set of citrus(orange) lovers. Since everyone loves at least one kind of fruit, the total number of fruit lovers in the universe set = 100.

We can use the formula: n ( A ∪ B ∪ C ) = n ( A ) + n ( B ) + n ( C ) − n ( A ∩ B ) − n ( B ∩ C ) − n ( C ∩ A ) + n ( A ∩ B ∩ C ) n(A\cup B\cup C)\ = n(A) + n(B) + n(C) - n(A\cap B) - n(B\cap C) - n(C\cap A) + n(A\cap B\cap C)

Then we can plug in the numbers:

100 = 63 + 54 + 57 − 32 − 24 − 28 + n ( A ∩ B ∩ C ) 100 = 63 + 54 + 57 - 32 - 24 -28 + n(A\cap B\cap C) ; n ( A ∩ B ∩ C ) = 10 n(A\cap B\cap C) = 10 .

Therefore, there are 10 \boxed{10} people who love all kinds of fruits, and the data can be presented in the following Venn's diagram:

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Yes, the Venn diagram is the proper way to present this information.

I feel like the table will just be confusing to other people (or it could just be me).

Thank you for the review. I agree. Just a fun way to represent them, I guess. ;)

Worranat Pakornrat - 5 years, 3 months ago

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