What is the probability that P>Q>0

[goelmohit2002]

Hi All,

if x^2 + y^2 = r^2 is the equation of the circle with centre as origin and radius as r.

Point (P,Q) is randomly selected inside the above circle. What is the probability that P>Q>0 ?

OA = 1/8. Can someone please tell how the answer is 1/8....since on line y=x, the above inequality that is P>Q>0 is not satisfied.

[RonPurewal]

Hi All,

if x^2 + y^2 = r^2 is the equation of the circle with centre as origin and radius as r.

Point (P,Q) is randomly selected inside the above circle. What is the probability that P>Q>0 ?

OA = 1/8. Can someone please tell how the answer is 1/8....since on line y=x, the above inequality that is P>Q>0 is not satisfied.

two-dimensional probabilities are defined in terms of areas. this probability is therefore (area of region such that p > q > 0) / (total area).
since boundary lines/curves themselves have zero area, it doesn't make any difference whether you include them in the region. (i.e., if the problem said p>q>0, p>q>0, or p>q>0, the area would still be the same every time.)

the area in question is the area of the sector (pie slice) between the x-axis and the line y = x. by symmetry, one can see that this is exactly 1/8 of the circle.

--

are these sorts of probabilities even tested on the gmat? thinking back, the only probability problems i can remember are the ones with discrete events.

[goelmohit2002]

Hi All,

if x^2 + y^2 = r^2 is the equation of the circle with centre as origin and radius as r.

Point (P,Q) is randomly selected inside the above circle. What is the probability that P>Q>0 ?

OA = 1/8. Can someone please tell how the answer is 1/8....since on line y=x, the above inequality that is P>Q>0 is not satisfied.

two-dimensional probabilities are defined in terms of areas. this probability is therefore (area of region such that p > q > 0) / (total area).
since boundary lines/curves themselves have zero area, it doesn't make any difference whether you include them in the region. (i.e., if the problem said p>q>0, p>q>0, or p>q>0, the area would still be the same every time.)

the area in question is the area of the sector (pie slice) between the x-axis and the line y = x. by symmetry, one can see that this is exactly 1/8 of the circle.

--

Hi Ron,

Thanks.

Thanks....

for PS question yes it is fine...what if this info would have came in DS question....would only this info be sufficient to calculate the probability i.e. C or insufficient i.e E

[goelmohit2002]

are these sorts of probabilities even tested on the gmat? thinking back, the only probability problems i can remember are the ones with discrete events.

Hi Ron,

Can you please elaborate a bit more what exactly you meant to say here.

Thanks
Mohit

[Ben Ku]

The sample question posed is a "geometric probability" type question. In fact, it's more of a fraction question rather than a probability question. A way to rephrase this question is to ask: "What fraction of a circle centered at the origin is in the first quadrant and beneath the line y = x?"

This is different from "discrete probabilities" where we're talking about the probabilities of events:
What is the probability of selecting a king from a deck of cards?
If three coins are tossed, what is the probability of having at least one heads?
If there's a 30% chance that Joe will win, and 60% chance that Sue will win, what is the probability that they both do not win?

I think Ron means that there's a greater probability of seeing a discrete probability question on the GMAT than a geometric probability. Hope that helps.