Question

How to draw this venn diagram please and also explain ur steps how u got the numbers

Answer 1

See the diagram at the end of the explanation

Explanation

Given that the total number of surveyed people is 30 and 2 people don't like chocolate or vanilla ice creams, then 28 (= 30 - 2) people like at least one of these flavors.

Considering only the people who at least like one of the flavors, the next Venn diagram can be drawn:

where:

`\begin{gathered} x+y+z=28\text{ \lparen number of people who like at least one flavor\rparen} \\ x+y=22\text{ \lparen number of people who like chocolate\rparen} \\ y+z=18\text{ \lparen number of people who like vanilla\rparen} \end{gathered}`

Combining the first and second equations, we get:

`\begin{gathered} 22+z=28 \\ z=28-22 \\ z=6 \end{gathered}`

Combining the first and third equations, we get:

`\begin{gathered} x+18=28 \\ x=28-18 \\ x=10 \end{gathered}`

Substituting these results into the first equation:

`\begin{gathered} 10+y+6=28 \\ 16+y=28 \\ y=28-16 \\ y=12 \end{gathered}`

Now, with these results we can draw the Venn diagram as follows (where the "2" outside the circles indicates the number of people who don't like chocolate or vanilla):