Name__________________

Homework February 8, 2005

 

 

 

Your top drawer contains 20 white socks and 10 black socks.

  1. You draw two socks at random without replacement. What is the probability they are the same color?

    2.  

     

     

     

  2. You draw four socks at random without replacement. What is the probability you draw two white socks and two black socks?

    3.  

     

     

  3. You draw all the socks one at a time without replacement. What is the probability the first and last socks are the same color?

    4.  

     

     

    Your middle drawer contains 6 white socks, 6 black socks, 6 orange socks, 6 green socks, and 6 purple socks.

  4. You draw two socks at random without replacement. What is the probability they are the same color?

    5.  

     

     

  5. You draw four socks at random without replacement. What is the probability they are all different colors?

    6.  

     

     

  6. You draw four socks at random without replacement. What is the probability exactly two colors are represented?

    7.  

     

     

  7. You draw one set of four socks and one set of two socks at random and without replacement. What is the probability both sets are all of the same color and each set is a different color?

    8.  

     

     

    Your bottom drawer contains 18 black socks, 18 red socks, and 2 green socks.

  8. You draw two socks at random and without replacement. What is the probability they are both the same color?

    9.  

     

     

  9. Your friend offers to pay you 1 to 1 if you achieve the goal of problem 8? What is the expected value (to you) of this bet?

    10.  

     

     

  10. You draw three socks at random. What is the probability they are all different colors?

    11.  

     

     

     

  11. Your older sister offers 12 to 1 odds that you can achieve the goal of problem 10. What is the house (or sister’s) advantage of this bet?

 

 

 

Extra Credit: Your brother has two sock drawers. One has one black sock and one white sock. The other has two black socks. However you don’t know which drawer has which socks. You open a drawer at random and pick a sock at random. You see the sock is black. What is the probability the other sock in the same drawer is also black?