geometrical probability

juantheron · 2011-12-14 08:00:23

a point

is selected at random in a sphere. then find the probability that the point is closer to the

center of the sphere than to its surface

bobbym · 2011-12-14 08:05:09

Hi;

TheDude · 2011-12-14 08:09:39

Assuming that all points are equally likely to be chosen, the probability of P being in any particular section of the sphere is equal to the ratio of the volume of that section to the volume of the entire sphere. If we assume the sphere has radius 1, then we want to find the probability that P is within 1/2 of the center, so the probability U that P is closer to the center than the surface is

juantheron · 2011-12-14 08:19:59

thanks bobbym and Dude

but for radius of 1unit, If we take a sphere of radius 1/2

than the point which is exactly on that sphere(1/2 radius sphere) . then these point are equal distance from center of sphere of radius 1 and also equal distance from surface

bobbym · 2011-12-14 08:22:08

We are equating volumes the surface of the inner sphere does not have a volume. It does not have any depth. It is two dimensional therefore no volume.

juantheron · 2011-12-14 08:36:12

bobbym i want more explanation

thanks

bobbym · 2011-12-14 08:43:54

What is the question?

juantheron · 2011-12-14 09:13:42

the line

We are equating volumes the surface of the inner sphere does not have a volume. It does not have any depth. It is two dimensional therefore no volume.

TheDude · 2011-12-14 11:12:38

Even though there is a possibility that the point P will land exactly at the halfway point between the center and the surface of the sphere, in a mathematical sense the probability of this happening is exactly 0. So there's no need to consider this possibility when answering this question.

Math Is Fun Forum

#1 2011-12-14 08:00:23

geometrical probability

#2 2011-12-14 08:05:09

Re: geometrical probability

#3 2011-12-14 08:09:39

Re: geometrical probability

#4 2011-12-14 08:19:59

Re: geometrical probability

#5 2011-12-14 08:22:08

Re: geometrical probability

#6 2011-12-14 08:36:12

Re: geometrical probability

#7 2011-12-14 08:43:54

Re: geometrical probability

#8 2011-12-14 09:13:42

Re: geometrical probability

#9 2011-12-14 11:12:38

Re: geometrical probability

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