goelmohit2002 Wrote: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.
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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.