Solution: 2015 Fall Final - 5

Author: Michiel Smid

Question

In a group of 30 people,

How many people in this group are blond and have green eyes?

(a)

(b)

(c)

(d)

Let S be the set of all people in the group.
The size of S is the number of people in the group: $ |S| = 30 $
Let A be the event that a person is blond.
$ |A| = 10 $
Let B be the event that a person has green eyes.
$ |B| = 20 $
Let $ \overline{A \cup B} $ be the event that a person is not blond and does not have green eyes.
$ |\overline{A \cap B}| = 9 $
$ |A \cup B| = |S| - |\overline{A \cap B}| $
$ |A \cup B| = 30 - 9 $
$ |A \cup B| = 21 $
Let $A \cap B$ be the event that a person is blond and has green eyes.
$ |A \cup B| = |A| + |B| - |A \cap B| $
$ 21 = 10 + 20 - |A \cap B| $
$ |A \cap B| = 10 + 20 - 21 $
$ |A \cap B| = 9 $