Solution: 2017 Winter Final - 6
Author: Michiel SmidQuestion
Consider a group of 100 students. In this group,
- 63 students like beer,
- 71 students like cider, and
- 25 students do not like beer and do not like cider.
(a)
58
(b)
60
(c)
57
(d)
59
Solution
- Let B be the event that a student likes beer
$ |B| = 63 $ - Let C be the event that a student likes cider
$ |C| = 71 $ - Let's determine $ \overline{B} \cap \overline{C} $
$ | \overline{B} \cap \overline{C} | = 25 $
Now, let’s determine $ B \cup C $
$ B \cup C = 100 - | \overline{B} \cap \overline{C} | $
$ B \cup C = 100 - 25 $
$ B \cup C = 75 $
Finally, we can determine $ B \cap C $
$ B \cup C = |B| + |C| - |B \cap C| $
$ 75 = 63 + 71 - |B \cap C| $
$ 75 = 134 - |B \cap C| $
$ |B \cap C| = 59 $