The question is from:
https://www.beatthegmat.com/mba/2011/03/ ... 4-mar-2011
Three points are chosen independently an at random on the circumference of a circle with radius r. What is the approximate probability that none of the three points lies more than a straight-line distance of r away from any other of the three points?
(A) 1/9
(B) 1/12
(C) 1/18
(D) 1/24
(E) 1/27
B
My question:
According to the explanation, the probability of the first point is 1 and the probability of the second point is 1/3, since point 2 can be within 60 degrees from each side of point 1. BUT, in order for point 3 to have 1/6 probability, point 2 must be a point exactly 60 degrees away from either side of point 1. This means that the probability of the second point cannot be 1/3, because 1/3 means that there is a 1/3 chance point 2 can be anywhere within 60 degrees on each side of point 1, when in actuality point 2 can only be a point that is exactly 60 degrees away from either side of the first point. Thus, I believe point 2 cannot have a probability of 1/3.
Its the same thing with the lower limit that has a probability of 1/9. (1 * 1/3 * 1/3) If point 3 can be within 60 degrees away from each side of point 1 (thus the probability of point 3 is 1/3), then point 2 must be on the same point as point 1; this means that point 2 cannot have a probability of 1/3 because it cannot be any point within 60 degrees on each side of point 1, it must be exactly on point 1.
I knows its kind of hard to explain what I am saying without drawing a figure, but can anybody answer my question?
Thanks!
https://www.beatthegmat.com/mba/2011/03/ ... 4-mar-2011
Three points are chosen independently an at random on the circumference of a circle with radius r. What is the approximate probability that none of the three points lies more than a straight-line distance of r away from any other of the three points?
(A) 1/9
(B) 1/12
(C) 1/18
(D) 1/24
(E) 1/27
B
My question:
According to the explanation, the probability of the first point is 1 and the probability of the second point is 1/3, since point 2 can be within 60 degrees from each side of point 1. BUT, in order for point 3 to have 1/6 probability, point 2 must be a point exactly 60 degrees away from either side of point 1. This means that the probability of the second point cannot be 1/3, because 1/3 means that there is a 1/3 chance point 2 can be anywhere within 60 degrees on each side of point 1, when in actuality point 2 can only be a point that is exactly 60 degrees away from either side of the first point. Thus, I believe point 2 cannot have a probability of 1/3.
Its the same thing with the lower limit that has a probability of 1/9. (1 * 1/3 * 1/3) If point 3 can be within 60 degrees away from each side of point 1 (thus the probability of point 3 is 1/3), then point 2 must be on the same point as point 1; this means that point 2 cannot have a probability of 1/3 because it cannot be any point within 60 degrees on each side of point 1, it must be exactly on point 1.
I knows its kind of hard to explain what I am saying without drawing a figure, but can anybody answer my question?
Thanks!
