Results 1 to 4 of 4

Math Help - Probability (point on circle)

  1. #1
    Junior Member
    Joined
    Jan 2010
    From
    Florida
    Posts
    28

    Probability (point on circle)

    I have a word problem that is vexing me; the language is getting in the way of my reasoning...

    "Let's say we have a circle with a circumference of 10. A tack will be placed somewhere along the circumference of this circle. What is the likelihood it will be placed at the top half of the circumference? What is the likelihood it will placed at exactly the top of the circumference?"

    Presumably, the answer to the first question is .5

    But what does 'exactly at the top' mean? Couldn't there be an infinite number of places around the circumference for the tack (as no units of measurement are provided)? And how does one determine the top?

    Is this a trick logic question or am I missing something?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Quixotic View Post
    I have a word problem that is vexing me; the language is getting in the way of my reasoning...

    "Let's say we have a circle with a circumference of 10. A tack will be placed somewhere along the circumference of this circle. What is the likelihood it will be placed at the top half of the circumference? What is the likelihood it will placed at exactly the top of the circumference?"

    Presumably, the answer to the first question is .5

    But what does 'exactly at the top' mean? Couldn't there be an infinite number of places around the circumference for the tack (as no units of measurement are provided)? And how does one determine the top?

    Is this a trick logic question or am I missing something?
    The answer to the second part is zero. Consider if it had instead had asked what is the probability of it is placed on an arc that subtends x radians from the centre, then (assuming a uniform distribution on the circumference, which you should have specified) the probability is x/(2\pi).

    Now as x \to 0 this probability goes to zero.

    (as a general rule with a continuous probability distribution the probability of an discrete value occuring is zero)

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2010
    From
    Florida
    Posts
    28
    Quote Originally Posted by CaptainBlack View Post

    Now as x \to 0 this probability goes to zero.

    (as a general rule with a continuous probability distribution the probability of an discrete value occuring is zero)

    CB
    I'm grateful for the answer, but I still do not understand the reasoning behind it. Incidentally, I quoted the question from my worksheet exactly. No additional information was provided (and this isn't from a statistics course!).

    My new question is this: how does one know or 'prove' that the probability of a discrete value occuring is zero? This sounds like one of those general principles I need to remember, but I don't understand it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Quixotic View Post
    I'm grateful for the answer, but I still do not understand the reasoning behind it. Incidentally, I quoted the question from my worksheet exactly. No additional information was provided (and this isn't from a statistics course!).

    My new question is this: how does one know or 'prove' that the probability of a discrete value occuring is zero? This sounds like one of those general principles I need to remember, but I don't understand it.
    Well if it says no more than you report the only correct answer is that there is insufficient data.

    Essentially for a continuous random variable what I posted is the proof, with a minor modification for distributions other than the uniform. Though if you wait long enough someone will be along with a measure theory proof.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Point on Circle Closest to Another Point on Circle
    Posted in the Geometry Forum
    Replies: 8
    Last Post: September 20th 2011, 06:21 AM
  2. Circle, tangent line, and a point not on the circle
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: March 31st 2011, 02:40 PM
  3. Point along a circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 2nd 2009, 01:51 AM
  4. Point Circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: February 23rd 2008, 08:55 PM
  5. 9-point circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 11th 2006, 03:52 PM

Search Tags


/mathhelpforum @mathhelpforum