An interesting experiment
There are two balls, one yellow and one blue, in a box.
Do the following:
1.Pick up one randomly from the box to see the color and
put it again into the box.
2.If it is yellow, then add another yellow ball in the box; if it is blue, add
another blue ball in the box.
3.Repeat the above steps until there are 4000 balls in the box.
4.Count the number of yellow balls and blue balls and calculate the proportion of the
yellow one. Write it down.
5.Do the above experiment 2000 times and find the distribution of the ratio.
It is boring, isn't it? OK, let the computer do it.
What do you expect the result?
(Most people think the proportion of yellow balls will go to either 1 or 0. Do you think so?)
The result, simulated by computer:
a. the initial number of the yellow and blue is 1 and 1, respectively.
The proportion of yellow balls goes neither to 1 nor 0. In fact it's evenly distributed.
b. the initial number of the yellow and blue is 2 and 1, respectively.
c. the initial number of the yellow and blue is 3 and 1, respectively.
d. the initial number of the yellow and blue is 2 and 2, respectively.
e. the initial number of the yellow and blue is 3 and 3, respectively.
