Results 1 to 3 of 3

Math Help - What are the chances?

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    1

    What are the chances?

    You have 30 students in a class. All 30 names are put into a hat. One name is drawn out then put back in for a second drawing. What are the chances of drawing the same name both times?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Mar 2008
    Posts
    182
    Quote Originally Posted by mulkeyjb View Post
    You have 30 students in a class. All 30 names are put into a hat. One name is drawn out then put back in for a second drawing. What are the chances of drawing the same name both times?
    1/30

    Your first choice can be any name, ie. a 30/30 chance. And then your second choice can only be that one name, ie. a 1 in 30 chance.
    Ergo: (30/30)*(1/30)=(1/30)

    Now - if you wanted a particular name to come out, before the first selection, that would be 1/30 * 1/30 = 1/900.

    Or if you don't replace the name... well... then you're in trouble...
    Last edited by Unenlightened; May 5th 2008 at 09:08 AM. Reason: expanding...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    GAMMA Mathematics
    colby2152's Avatar
    Joined
    Nov 2007
    From
    Alexandria, VA
    Posts
    1,172
    Awards
    1
    Quote Originally Posted by mulkeyjb View Post
    You have 30 students in a class. All 30 names are put into a hat. One name is drawn out then put back in for a second drawing. What are the chances of drawing the same name both times?
    Well, think...

    There is a 1 in 30 chance a given student's name is drawn. If you put their card back into the hat, then the set of possible events remains the same, so the chances stay the same.

    The probability of drawing a given name twice is equal to \left(\frac{1}{30}\right)^2 = \frac{1}{900}

    The probability of drawing the same name twice considers the possibility of drawing any of the other 29 students' names twice in a row. That gives our probability 30 different ways of happening.

    30*\frac{1}{900} = \frac{1}{30}

    Our answer for two is the same as one, but why?

    Well... if we are looking in GENERAL for the same student picked twice, then it doesn't matter which student is picked the 1st time (p = 100%) as long as they are picked the 2nd time (1 in 30).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. what are the chances of a heads...
    Posted in the Statistics Forum
    Replies: 2
    Last Post: April 17th 2011, 04:38 AM
  2. chances of making it into top 10%
    Posted in the Statistics Forum
    Replies: 3
    Last Post: March 11th 2010, 02:21 PM
  3. [SOLVED] chances
    Posted in the Statistics Forum
    Replies: 1
    Last Post: September 16th 2009, 02:49 PM
  4. What are the chances?
    Posted in the Statistics Forum
    Replies: 3
    Last Post: June 28th 2008, 04:31 AM
  5. what are the chances?
    Posted in the Statistics Forum
    Replies: 6
    Last Post: January 14th 2006, 05:43 PM

Search Tags


/mathhelpforum @mathhelpforum