I12-39

Question

A bag contains 20 fruits of three types: apples, bananas, and oranges. Each type appears in a different quantity. The probability of picking any type of fruit is greater than  \frac{1}{5}  but less than  \frac{1}{2} .
 
Select for  Certain  a number that must represent the count of one type of fruit in the bag, and select for  Minimum  a number that represents the smallest possible count of a type of fruit. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Since the probability of picking any type of fruit is greater than  \frac{1}{5}  but less than  \frac{1}{2} , the count of each type must be more than 4 and less than 10. This means each type has a count of 5, 6, 7, 8, or 9.
 
If the highest count is 9, the next highest can only be 6 (any other value would leave less than 5 for the third type), making the third count 5.
 
If the highest count is 8, the next highest can only be 7, making the third count 5.
 
The highest count cannot be 7 or less because, in that case, the total cannot reach 20 (e.g., 7 + 6 + 5 = 18).
 
Hence, the only possible distributions of fruits are (9, 6, 5) or (8, 7, 5).
 
Thus, a number that  must  represent the count of one type of fruit in the bag is 5, and the smallest possible count of a type of fruit is also 5.

Correct answer:

Certain  "5"

Minimum  "5"

Bunuel · Answer

I have revised the question, solution, and formatting by adding more details to enhance clarity.

Dereno · Answer

Another interesting question 👍☺️

happysisyphus · Answer

Really good question.. Though I missed it in my first attempt.

agrasan · Answer

I like the solution - it’s helpful.

Vivek1707 · Answer

This is a great question that’s helpful for learning.

ShubhangKedia · Answer

This is a great question that’s helpful for learning and I like the solution - it’s helpful.

cdb · Answer

I like the solution - it’s helpful.

Pikachuu · Answer

I like the solution - it’s helpful. Innovative question with a nuance

blablabla1234 · Answer

I like the solution - it’s helpful.

SoftRat · Answer

I like the solution - it’s helpful.

I12-39

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