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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.

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    $\begingroup$ Welcome to the site. What have you tried? $\endgroup$
    – N. F. Taussig
    Oct 20, 2014 at 18:13
  • $\begingroup$ 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. $\endgroup$
    – Lucia
    Oct 20, 2014 at 18:23
  • $\begingroup$ Your last bullet point does not bear on the question of how to draw the Venn diagram. $\endgroup$
    – Michael Hardy
    Jul 30, 2017 at 18:28

1 Answer 1

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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 $M \cap B$).

Without more information about whether the class monitor is male or female and does or does not have blue eyes, it is not possible to include the set of class monitors in the diagram.

Venn_diagram_of_male_and_female_students_with_and_without_blue_eyes

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