Results 1 to 3 of 3

Math Help - Probability- pick 10 numbers from 1-100

  1. #1
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    Probability- pick 10 numbers from 1-100

    Hi all,

    You choose a number at random from the numbers 1-100 ten times. What is the probability of choosing 10 distinct numbers? What is the probability that the first number chosen is larger than each of the other nine numbers chosen?


    So, for the first question, I compute the following- (100*99*98*97*96*95*94*93*92*91)/(100^10) = .628

    For the second question, I can either first draw a one, OR a two, OR a three. If I draw a 1, nothing is lower so the probability is 0. If I draw a 100, 99 numbers are lower. So, I perform the following calculation-

    SUM (1/100) * ((n/100)^9) for n = 1 to 99.

    This is equivalent to saying "probability I first draw number n AND I subsequently draw 9 numbers lower than it"

    I get .095. Is this correct? Is there a better way?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1

    Re: Probability- pick 10 numbers from 1-100

    Quote Originally Posted by sfspitfire23 View Post
    Hi all,

    You choose a number at random from the numbers 1-100 ten times. What is the probability of choosing 10 distinct numbers? What is the probability that the first number chosen is larger than each of the other nine numbers chosen?
    So, for the first question, I compute the following- (100*99*98*97*96*95*94*93*92*91)/(100^10) = .628
    For the second question, I can either first draw a one, OR a two, OR a three. If I draw a 1, nothing is lower so the probability is 0. If I draw a 100, 99 numbers are lower. So, I perform the following calculation-
    SUM (1/100) * ((n/100)^9) for n = 1 to 99.
    This is equivalent to saying "probability I first draw number n AND I subsequently draw 9 numbers lower than it"
    I get .095. Is this correct? Is there a better way?
    The reason I deleted my reply is that it is not clear to me from the wording of the question if the numbers are distinct as in part #1 or not.

    I do agree with you on that part.

    Are they distinct or not?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member sfspitfire23's Avatar
    Joined
    Oct 2009
    Posts
    273

    Re: Probability- pick 10 numbers from 1-100

    The numbers do not have to be distinct in the second part of the question
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 9th 2012, 08:43 AM
  2. Probability to pick same book
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 6th 2011, 08:03 PM
  3. Replies: 1
    Last Post: August 29th 2011, 02:18 AM
  4. Replies: 1
    Last Post: September 24th 2010, 02:47 PM
  5. Help me pick a topic!
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: September 18th 2008, 04:51 PM

Search Tags


/mathhelpforum @mathhelpforum