The sum of slip is 9 small coffee order, then sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.
Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
A hat contains 4 slips of paper labeled as 3,3,6 and 8. One slip is selected randomly and without replacing, another one is selected. The number on the slips are added together.
The probability of getting a sum of 6 (3+3) is,
[tex]P_(3,3)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(3,3)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(3,3)=\dfrac{2}{12}\\P_(3,3)=\dfrac{1}{6}[/tex]
The probability of getting the sum of 9 (6+3) or (3+6) is,
[tex]P_(3,6)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,6)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,6)=\dfrac{4}{12}\\P_(3,6)=\dfrac{1}{3}[/tex]
The probability of getting the sum of 9 (6+3) or (3+6) is,
[tex]P_(3,8)=\dfrac{1}{4}\times\dfrac{2}{3}+\dfrac{2}{4}\times\dfrac{1}{3}\\P_(3,8)=\dfrac{2}{12}+\dfrac{2}{12}\\P_(3,8)=\dfrac{4}{12}\\P_(3,8)=\dfrac{1}{3}[/tex]
The probability of getting a sum of 6 (3+3) is,
[tex]P_(6,8)=\dfrac{1}{4}\times\dfrac{1}{3}+\dfrac{1}{3}\times\dfrac{1}{4}\\P_(6,8)=\dfrac{1}{12}+\dfrac{1}{12}\\P_(6,8)=\dfrac{2}{12}\\P_(6,8)=\dfrac{1}{6}[/tex]
There are three size of coffee to order:
Thus, when the sum of slip is 9 small coffee order, if sum is 11 medium coffee order, and when the sum is 6 or 14 large coffee is ordered.
Learn more about the arrangement here;
https://brainly.com/question/6032811
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