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?

A. 50%
B. 25%
C. 16 2/3%
D. 12 1/2%
E. 0%

These are all the possible combinations:

S takes a hard chair
DGRS--1/6
GRDS--1/6

D takes a hard chair
SGRD--1/6
GRSD--1/6

R takes a hard chair
SDGR--1/12
DSGR--1/12

G takes a hard chair
SDRG--1/12
DSRG--1/12

Therefore, the probability that Darcy will sit in a hard chair is 1/3 and the probability that Darcy will sit in a soft chair is 2/3

And the probability that Gina will sit in a hard chair is 1/6 and the probability that Gina will sit in a soft chair is 5/6.

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? . This is a ticky question to answer as the first probablity is lower than the second one.

I would answer 0.

If the question were asking the opposite, ie by what percent the probability that Gina will sit in a soft chair greater than the probability that dary will sit in a soft chair is, the answer would be 25%.

The probablity that Gina arrives third and does not get a soft chair really depends on whether Darcy and Ray want to take up a soft chair at all Doesnt it?

If Susan comes first, and picks the hard chair, then it doesn't really matter if Gina comes third or even last since she will always gets soft chair in this instance. To me, this question has a lot of assumptions.

I believe that your last step should just be 1/6*100% = 16.66%. We're asking percentage differecne and since we already found the difference (by subtracting the probability), then we should just conver it to a percentage change.

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
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Because we have to find how much higher is D's probability (of getting a soft chair) than G's one. Not the absolute difference between the two probablities. Is it clear ?
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