# Venn- Diagrams, Probability

I want to know how to draw a Venn Diagram with the given information below..

There are 30 students:

• 16 are girls;
• There are 7 girls and 6 boys who have blue eyes.
• A student is randomly chosen to be class monitor.

Draw a Venn Diagram to represent this information.

### Progress

I thought a possible answer would be 2 separate circles, one for boys and one for girls. Each one of the circles would have a smaller circle inside, with the total of each with blue eyes. For example, the girl's would have 8 in the large circle and 6 in the smaller circle situated inside of the larger one. And for the boys, there would be 9 in the large and 7 in the smaller circle. According to some, it wouldn't qualify as a Venn-Diagram, so I don't know if it's correct.

• Welcome to the site. What have you tried? Oct 20, 2014 at 18:13
• Hi, thanks :) I thought a possible answer would be 2 separate circles, one for boys and one for girls. Each one of the circles would have a smaller circle inside, with the total of each with blue eyes. For example, the girl's would have 8 in the large circle and 6 in the smaller circle situated inside of the larger one. And for the boys, there would be 9 in the large and 7 in the smaller circle. According to some, it wouldn't qualify as a Venn-Diagram, so I don't know if it's correct. Oct 20, 2014 at 18:23
• Your last bullet point does not bear on the question of how to draw the Venn diagram. Jul 30, 2017 at 18:28

You are correct that you should draw separate circles for the boys and girls. In the diagram below, I have labeled them $M$ for males and $F$ for females. However, all of the people with blue eyes should be in one set that intersects with the sets for males and females. I labeled this set $B$ for blue eyes. The nine girls who do not have blue eyes are shown in the red region; the seven girls who do have blue eyes are in the magenta region where the set of females intersects the set of people who have blue eyes (the set $F \cap B$). The eight boys who do not have blue eyes are in the green region; the six boys who do have blue eyes are in the cyan region where the set of males intersects the set of people who have blue eyes (the set $M \cap B$).