# Thread: This question is mind blow. Can anyone help this out? Really appreciate it.

1. ## This question is mind blow. Can anyone help this out? Really appreciate it.

The Owner of a convenience store reports that of 890 people who bought bottled fruit juice in a recent week.
l 750 bought orange juice
l 400 bought apple juice
l 100 bought grapefruit juice
l 50 bought citrus punch.
l 328 bought orange juice and apple juice
l 25 bought orange juice and grapefruit juice
l 12 bought orange juice and citrus punch.
l 35 bought apple juice and grapefruit juice.
l 8 bought apple juice and citrus punch.
l 33 bought grapefruit juice and citrus punch.
l 4 bought orange juice, apple juice and citrus punch.
l 17 bought orange juice, apple juice and grapefruit juice.
l 2 bought citrus punch, apple juice and grapefruit juice.
l 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: This question is mind blow. Can anyone help this out? Really appreciate it.

Originally Posted by zackryilmi96
The Owner of a convenience store reports that of 890 people who bought bottled fruit juice in a recent week.
l 750 bought orange juice
l 400 bought apple juice
l 100 bought grapefruit juice
l 50 bought citrus punch.
l 328 bought orange juice and apple juice
l 25 bought orange juice and grapefruit juice
l 12 bought orange juice and citrus punch.
l 35 bought apple juice and grapefruit juice.
l 8 bought apple juice and citrus punch.
l 33 bought grapefruit juice and citrus punch.
l 4 bought orange juice, apple juice and citrus punch.
l 17 bought orange juice, apple juice and grapefruit juice.
l 2 bought citrus punch, apple juice and grapefruit juice.
l 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.
We use $\|a\|$ to be the number buying apple juice.
$\begin{array}{l}\|o\vee a\vee g\vee c\|=\|o\|+\|a\|+\|g\|+\|c\|\\-\|o\wedge a\|-\|o\wedge g\|-\|o\wedge c\|-\|g\wedge a\|-\|c\wedge a\|-\|c\wedge g\| \\ + \|o\wedge a\wedge c \|+\|o\wedge a\wedge g\|+\|c\wedge a\wedge g\|+\|o\wedge g\wedge c\|\\-\|o\wedge g\wedge a\wedge c\|\end{array}$