Drawing Venn Diagrams Effectively

Two Circles

There are $50$ students in a certain high school. $16$ study Physics, $13$ study Chemistry, and $15$ study both Physics and Chemistry. Illustrate this information on a Venn diagram.

\begin{align} a+b+c+d &= 50 \text{ total students} \\ a+b &= 31 \text{ Physics} \\ b+c &= 28 \text{ Chemistry} \\ b &= 15 \text{ Physics and Chemistry} \end{align}

\begin{align} \text{Substitute } b &=15 \text{ into } a+b=31 \\ a+15 &= 31 \\ a &= 16 \end{align}

\begin{align} \text{Substitute } b &=15 \text{ into } b+c=28 \\ 15+c &= 28 \\ c &= 13 \end{align}

\begin{align} \text{Substitute } a =16, b=15, c &=13 \text{ into } a+b+c+d=50 \\ 16 +15+13+d &= 50 \\ d &= 6 \end{align}

Three Circles

Now, let’s take a look at a situation with three circles.

A school has three subjects offered: Arts, Biology and Chemistry.

$36$ students chose Arts, $39$ chose Biology, and $37$ chose Chemistry. Of those, $9$ chose both Arts and Biology, $12$ chose both Biology and Chemistry, and $11$ chose both Arts and Chemistry. $5$ chose all three subjects.

$$a=5$$

\begin{align} a+d &= 9 \\ 5+d &= 9 \\ d &= 4 \end{align}

\begin{align} a+b &= 12 \\ 5+b &= 12 \\ b &= 7 \end{align}

\begin{align} a+c &= 11 \\ 5+c &= 11 \\ c &= 6 \end{align}

\begin{align} g+4+5+6 &= 36 \\ g &= 21 \end{align}

\begin{align} e + 4+5+7 &= 39 \\ e &= 23 \end{align}

\begin{align} f + 6+5+7 &= 37 \\ f &= 19 \end{align}

\begin{align} h &= 100-(21+4+5+6+7+23+19) \\ &= 15 \end{align}

âœ“ Discover more enlightening videos by visiting our YouTube channel!

The Best Practices for Using Two-Way Tables in Probability

Welcome to a comprehensive guide on mastering probability through the lens of two-way tables. If you’ve ever found probability challenging, fear not. We’ll break it…

Mastering Probability: Venn Diagrams Made Easy

Visualising multiple events using Venn diagrams to find probabilities is done quite often. Welcome to this comprehensive guide on mastering probability using Venn Diagrams. Whether…

Mastering Integration by Parts: The Ultimate Guide

Welcome to the ultimate guide on mastering integration by parts. If you’re a student of calculus, you’ve likely encountered integration problems that seem insurmountable. That’s…

High School Math for Life: Making Sense of Earnings

Salary Salary refers to the fixed amount of money that an employer pays an employee at regular intervals, typically on a monthly or biweekly basis,…

Induction Made Simple: The Ultimate Guide

“Induction Made Simple: The Ultimate Guide” is your gateway to mastering the art of mathematical induction, demystifying a powerful tool in mathematics. This ultimate guide…