The Nature of Mathematics, 12th Edition
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Chapter 16 Projects

Section 16.2 Individual Research

Individual Research Project 16.2

Five identical containers (shoe boxes, paper cups, etc.) must be prepared for this problem, with contents as follows: 

There are five boxes containing red and white items (such as marbles, poker chips, or colored slips of paper).
                         Box                     Contents
                          #1             15 red and 15 white
                          #2             30 red and 0 white
                          #3             23 red and 5 white
                          #4             20 red and 10 white
                          #5             10 red and 20 white
    Select one of the boxes at random so that you don't know its contents.
    Step  1  Shake the box.
    Step  2  Select one marker, note the result, and return it to the box.
    Step  3  Repeat the first two steps 20 times with the same box.

a.  What do you think is inside the box you have sampled?
b.  Could you have guessed the contents by repeating the experiment five times?  Ten times?  Do you think you should have more than 20 observations per experiment?