Darcy, Gina, Ray and Susan will be the only participants at a meeting.

We will do:

Darcy = D
Ray = R
Susan = S
Gina = G

Keep in mind that follows:

1 Darcy and Ray arrive together at the location of the chairs.

2. the probability that Susan arrives first is 1/3 and the probability that Gina arrives first is also 1/3.

3. the probability that Gina comes last is 1/3 and the probability that Susan comes last also is 1/3.

1.-deduce that DR, come as a unit to the location of the chairs, so we will have three candidates (not four) arriving at the location of the chairs, these are: DR, S and G.

2.-given that there are three candidates for the position of the chairs, it follows that the probability of arriving first DR is 1/3.

3.-given that there are three candidates for the position of the chairs, it follows that the probability of arriving last DR is 1/3

We can also deduce from all of the above information to: as each of the three: DR, G or S, may become second and that between the probability that arrive in the first or the last place each of the three add 2/3, we conclude that each of the three has a probability of 1/3 in second place.

Thus we have arrival location of chairs

DR probability:

For 1st place = 1/3
For 2nd place = 1/3
For 3rd place = 1/3

Probability of S:

For 1st place = 1/3
For 2nd place = 1/3
For 3rd place = 1/3

Probability of G:

For 1st place = 1/3
For 2nd place = 1/3
For 3rd place = 1/3

So:

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 D on G accesses a soft Chair is:

100 x (5/6 - 4/6) /(4/6) = 25% correct response b)

hurtado Claudio gmat gre sat math preparation