Solution: 2016 Fall Final - 5

• Let S be the set of all students.
  $ |S| = 100 $
• Let C be the event that someone drinks cider
  $ |C| = 25 $
• Let B be the event that someone drinks beer
  $ |B| = 50 $
• Let $ \overline{C} \cap \overline{B} $ be the event that someone does not drink cider and does not drink beer
  $ | \overline{C} \cap \overline{B} | = 33 $

Find the union of C and B

$ |C \cup B| = |S| - | \overline{C} \cap \overline{B} | $

$ |C \cup B| = 100 - 33 $

$ |C \cup B| = 67 $

Now, we find the intersection of C and B

$ |C \cup B| = |C| + |B| - |C \cap B| $

$ 67 = 25 + 50 - |C \cap B| $

$ |C \cap B| = 8 $