Solution: 2015 Winter Final - 5
Author: Michiel SmidQuestion
In a group of 20 people,
- 6 are blond,
- 7 have green eyes,
- 11 are not blond and do not have green eyes.
(a)
4
(b)
5
(c)
3
(d)
6
Solution
- Let B be the event that someone is blond
$ |B| = 6 $ - Let G be the event that someone has green eyes
$ |G| = 7 $ - Let $ \overline{B} \cap \overline{G} $ be the event that someone is not blond and not green-eyed
$ | \overline{B} \cap \overline{G} | = 11 $
$ |B \cup G| = 20 - 11 = 9 $
$ |B \cup G| = |B| + |G| - |B \cap G| $
$ 9 = 6 + 7 - |B \cap G| $
$ |B \cap G| = 4 $