PASCAL 2012 Problem 25

There are four people in a room.
For every two people, there is a 50\% chance that they are friends.
Two people are connected if:

  • they are friends, or
  • a third person is friends with both of them, or
  • they have different friends who are friends of each other.

What is the probability that every pair of people in this room is connected?

Answer Choices
A. \frac{18}{32}
B. \frac{20}{32}
C. \frac{22}{32}
D. \frac{19}{32}
E. \frac{21}{32}