Question

A survey of few student what the drink in the morning ?

Use a Venn diagram to answer the following question. A survey of students in Math 2000 reveals the following information regarding consumption of hot beverages in the morning. 23 students drink tea, 51 drink coffee, 27 drink instant soup, 4 drink tea and coffee, 9 drink tea and soup,11 drink coffee and soup, 1 drinks all three, and 13 don't drink any of these 2 beverages in the morning.

a) Based on the information given, how many students were surveyed?
b) How many drink coffee but not tea nor soup?
c) How many drink tea and soup?
d) How many drink exactly one drink?

Answer 1

Please see below.

Explanation:

The results of the survey are shown in the following diagram.

Here those drinking `color(green)("Tea")` are included in green colored circle, those drinking `color(brown)("Coffee")` are included in brown colored circle and those drinking `color(pink)"Soup"` are included in peach colored circle.

The common areas that are shared between circles, show those drinking two or more than two drinks. For example `1` drinks all the three, `4` drink tea and coffee, `11` drink coffee and there are `51` drinking coffee, `51-(1+4+11)=51-16=35` drink only two. Similarly, `23` drink tea, but as `4` drink tea and coffee, `1` drinks all tree and `9` drink tea and soup, those drinking only tea are `23-1-4-9=9` only. Similarly `6` drink only soup.

As `13` do not drink any of these, they are shown outside the circles.

Hence,

(a) A total of `13+34+4+1+11+9+9+6=87` students were surveyed.
(b) `35` drink coffee but not tea nor soup.
(c) `9` drink tea and soup.
(d) `35+9+6=50` drink exactly one drink.