# Thread: Sets for 4 segment

1. ## Sets for 4 segment

Hope you all help me. I really appreciate it.

This is the question.

The Owner of a convenience store reports that of 890 people who bought bottled fruit juice in a recent week.
750 bought orange juice
400 bought apple juice
100 bought grapefruit juice
50 bought citrus punch.
328 bought orange juice and apple juice
25 bought orange juice and grapefruit juice
12 bought orange juice and citrus punch.
35 bought apple juice and grapefruit juice.
8 bought apple juice and citrus punch.
33 bought grapefruit juice and citrus punch.
4 bought orange juice, apple juice and citrus punch.
17 bought orange juice, apple juice and grapefruit juice.
2 bought citrus punch, apple juice and grapefruit juice.
9 bought orange juice, grapefruit juice and citrus punch.
Determine the numbers of people who bought
(a) all four kinds of juice.
(b) grapefruit juice, but nothing else.
(c) exactly two kinds of juice.
(d) more than two kinds of juice.
Draw the Venn diagram to represent each event.

2. ## Re: Sets for 4 segment

Originally Posted by aquhzie02
Hope you all help me. I really appreciate it.

This is the question.

The Owner of a convenience store reports that of 890 people who bought bottled fruit juice in a recent week.
750 bought orange juice
400 bought apple juice
100 bought grapefruit juice
50 bought citrus punch.
328 bought orange juice and apple juice
25 bought orange juice and grapefruit juice
12 bought orange juice and citrus punch.
35 bought apple juice and grapefruit juice.
8 bought apple juice and citrus punch.
33 bought grapefruit juice and citrus punch.
4 bought orange juice, apple juice and citrus punch.
17 bought orange juice, apple juice and grapefruit juice.
2 bought citrus punch, apple juice and grapefruit juice.
9 bought orange juice, grapefruit juice and citrus punch.
Determine the numbers of people who bought
(a) all four kinds of juice.
(b) grapefruit juice, but nothing else.
(c) exactly two kinds of juice.
(d) more than two kinds of juice.
Draw the Venn diagram to represent each event.
Use the letters $O,~A,~G,~\&~C$ to stand for who bought the particular flavor of juice.
\begin{align*}\|O\cup A\cup G\cup C\|&=890.\text{ those bought at least one }\\\|C\|&=50\\\|A\cap G\|&=35\\\|O\cap G\cap C\|&=9 \end{align*}

Now use inclusion/exclusion:
$\|O\cup A\cup G\cup C\|= \|O\|+ \|A\|+ \|G\|+\| C\|-\|O \cap A\|-\|O \cap G\|-\|O \cap C\|-\|A \cap G\|-\|A \cap C\|-\|G \cap C \|\\+\|O \cap A\cap G\|+\|O \cap A\cap C\|+\| A\cap G\cap C\|+\| Q\cap G\cap C\|-X$

TO FINISH YOU must find all other parts. Then solve for $X$.

3. ## Re: Sets for 4 segment

@aquhzie02, Please review what you have posted. I have worked with some of your data and found inconsistencies.
It may just be a matter of translation.

For example:
1) Do you mean that 500 bought citrus?
2) When it says "12 bought orange juice and citrus punch" does that mean only orange juice and citrus punch?
3) When it says "9 bought orange juice, grapefruit juice and citrus punch." does that mean only all three? OR those 9 included in the 12 above?