Darcy, Gina, Ray and Susan will be the only participants at a meeting. There will be three soft chairs in the room where the meeting will be held and one hard chair. No one can bring more chairs into the room. Darcy and Ray will arrive simultaneously, but Gina and Susan will arrive individually. The probability that Gina will arrive first is 1/3, and the probability that Susan will arrive first is 1/3. The probability that Gina will arrive last is 1/3, and the probability that Susan will arrive last is 1/3. Upon arriving at the meeting, each of the participants will select a soft chair, if one is available.
If Darcy and Ray arrive and see only one unoccupied soft chair, they will flip a fair coin to determine who will sit in that chair. By what percent is the probability that Darcy will sit in a soft chair greater than the probability that Gina will sit in a soft chair?	Choose one.
A) 50%
B) 25%
C) 16 2/3%
D) 12 1/2%
E) 0%
Location of D to access a soft Chair   If DR comes in first or second place both as R D they will access a soft Chair, this means that D in this situation has 1/3 + 1/3 to a soft Chair.   If DR comes third (last), D has a probability of (1/2) x (1/3) access to a soft Chair.   Then in all cases D has a probability of 1/3 + 1/3 + (1/2) x (1/3) = 5/6 access to a soft Chair.   Location of G to access a soft Chair   To G enter a soft Chair, you can only get in first or second place, if it reaches third we have addressed three soft chairs DR two soft chairs and S a soft Chair.   The probability that G arrives in first or second place is 1/3 + 1/3 = 2/3 = 4/6   Finally the highest percentage who 12 1/2% on G accesses a soft Chair is:   100 x (5/6 - 4/6) /(4/6) = 25%   ANSWER:12 1/2%
<result>D</result>
Darcy, Gina, Ray and Susan will be the only participants at a meeting. There will be three soft chairs in the room where the meeting will be held and one hard chair. No one can bring more chairs into the room. Darcy and Ray will arrive simultaneously, but Gina and Susan will arrive individually. The probability that Gina will arrive first is 1/3, and the probability that Susan will arrive first is 1/3. The probability that Gina will arrive last is 1/3, and the probability that Susan will arrive last is 1/3. Upon arriving at the meeting, each of the participants will select a soft chair, if one is available.
If Darcy and Ray arrive and see only one unoccupied soft chair, they will flip a fair coin to determine who will sit in that chair. By what percent is the probability that Darcy will sit in a soft chair greater than the probability that Gina will sit in a soft chair?