Results 1 to 4 of 4

Math Help - Dry cleaner & probability

  1. #1
    Newbie
    Joined
    Oct 2012
    From
    Americus
    Posts
    18

    Dry cleaner & probability

    The dry cleaner just delivered seventeen freshly cleaned different pairs of socks in a basket but the light bulb went out. The dry cleaner did not match the socks before delivery and I am in a hurry, so I blindly pick single socks from the basket. Is it possible that I actually will be wearing a matching pair of socks that evening after ten picks and how many times do I have to reach into that basket minimally to be guaranteed a matching pair of socks?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,973
    Thanks
    1121

    Re: Dry cleaner & probability

    Since there are seventeen different pairs of socks, it should be obvious that you can take seventeen socks out of the basket without getting a matched pair.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2012
    From
    Georgia
    Posts
    15

    Re: Dry cleaner & probability

    1. No, you have to pick at least 18 times from the basket to have a matching pair of socks.

    2. No, you have to pick at least three times from the basket to have a matching pair of socks.

    3. Yes, you have to pick at least two times from the basket to have a matching pair of socks. This is not very likely though.

    4. Yes, you have to pick at least one time from the basket to have a matching pair of socks. This is not very likely though.

    5. None of the above

    what would be the best option?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Dry cleaner & probability

    After picking the 1st single sock, remains 33 single socks. Now you start picking a 2nd single sock, if not as 1st then put it aside and pick 3rd single sock....repeating this 10 times for single sock=2,3,....11 we have the following increasing probabilities of picking the matching single sock to 1st sock:

    \begin{array}{rrrr}<br />
 {Sock= } & 2. & \text{ P[match 1st]= } & 0.030303 \\<br />
 \text{Sock= } & 3. & \text{ P[match 1st]= } & 0.03125 \\<br />
 \text{Sock= } & 4. & \text{ P[match 1st]= } & 0.0322581 \\<br />
 \text{Sock= } & 5. & \text{ P[match 1st]= } & 0.0333333 \\<br />
 \text{Sock= } & 6. & \text{ P[match 1st]= } & 0.0344828 \\<br />
 \text{Sock= } & 7. & \text{ P[match 1st]= } & 0.0357143 \\<br />
 \text{Sock= } & 8. & \text{ P[match 1st]= } & 0.037037 \\<br />
 \text{Sock= } & 9. & \text{ P[match 1st]= } & 0.0384615 \\<br />
 \text{Sock= } & 10. & \text{ P[match 1st]= } & 0.04 \\<br />
 \text{Sock= } & 11. & \text{ P[match 1st]= } & 0.0416667<br />
\end{array}

    these 10 picks sums to 0.3545 probability of finding the matching single sock.
    Attached Thumbnails Attached Thumbnails Dry cleaner &amp; probability-dry-cleaner-probability.png  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: July 11th 2012, 05:42 AM
  2. Replies: 10
    Last Post: January 21st 2011, 11:47 AM
  3. Replies: 3
    Last Post: May 29th 2010, 07:29 AM
  4. Replies: 1
    Last Post: February 18th 2010, 01:54 AM
  5. Replies: 3
    Last Post: December 15th 2009, 06:30 AM

Search Tags


/mathhelpforum @mathhelpforum