Unbias a random generator

Given a weighted one bit generator of random numbers where the probability of a one occuring, $P_{1}$ , is not the same as $P_{0}$ , the probability of a zero occuring. The probability of the occurrence of a one followed by a zero is $P_{1}\times P_{0}$ , which is the same as the probability of a zero followed by a one: $P_{0}\times P_{1}$ .

Task Details

Use your languages random number generator to create a function/method/subroutine/... randN that returns a one or a zero, but with one occurring, on average, 1 out of N times, where N is an integer from the range 3 to 6 inclusive.
Create a function unbiased that uses only randN as its source of randomness to become an unbiased generator of random ones and zeroes.
For N over its range, generate and show counts of the outputs of randN and unbiased(randN).

J

<lang j>biased=: 0 = ? unbiased=: i.@# { ::$: 2 | 0 3 -.~ _2 #.\ +: biased@# ]</lang>

Example use:

<lang j> biased 10#6 1 0 0 0 1 0 0 0 0 0

  unbiased 10#6

1 0 0 1 0 0 1 0 1 1</lang>

Python

<lang python>from __future__ import print_function import random

def randN(N):

   " 1,0 random generator factory with 1 appearing 1/N'th of the time"
   choose = [1] + [0] * (N-1)
   def rand():
       return random.choice( rand.choose )
   rand.choose = choose
   return rand

def unbiased(biased):

   'uses a biased() generator of 1 or 0, to create an unbiased one'
   this, that = biased(), biased()
   while this == that: # Loop until 10 or 01
       this, that = biased(), biased()
   return this         # return the first

if __name__ == '__main__':

   from collections import namedtuple

   Stats = namedtuple('Stats', 'count1 count0 percent')

   for N in range(3, 7):
       biased = randN(N)
       v = [biased() for x in range(1000000)]
       v1, v0 = v.count(1), v.count(0)
       print ( "Biased(%i)  = %r" % (N, Stats(v1, v0, 100. * v1/(v1 + v0))) )

       v = [unbiased(biased) for x in range(1000000)]
       v1, v0 = v.count(1), v.count(0)
       print ( "  Unbiased = %r" % (Stats(v1, v0, 100. * v1/(v1 + v0)), ) )</lang>

Sample output

Biased(3)  = Stats(count1=331800, count0=668200, percent=33.18)
  Unbiased = Stats(count1=499740, count0=500260, percent=49.973999999999997)
Biased(4)  = Stats(count1=249770, count0=750230, percent=24.977)
  Unbiased = Stats(count1=499707, count0=500293, percent=49.970700000000001)
Biased(5)  = Stats(count1=199764, count0=800236, percent=19.976400000000002)
  Unbiased = Stats(count1=499456, count0=500544, percent=49.945599999999999)
Biased(6)  = Stats(count1=167561, count0=832439, percent=16.7561)
  Unbiased = Stats(count1=499963, count0=500037, percent=49.996299999999998)

Tcl

<lang tcl># 1,0 random generator factory with 1 appearing 1/N'th of the time proc randN n {expr {rand()*$n < 1}}

uses a biased generator of 1 or 0, to create an unbiased one

proc unbiased {biased} {

   while 1 {

if {[set a [eval $biased]] != [eval $biased]} {return $a}

}

for {set n 3} {$n <= 6} {incr n} {

   set biased [list randN $n]
   for {set i 0;array set c {0 0 1 0}} {$i < 1000000} {incr i} {

incr c([eval $biased])

   }
   puts [format "  biased %d => #0=%d #1=%d ratio=%.2f%%" $n $c(0) $c(1) \

[expr {100.*$c(1)/$i}]]

   for {set i 0;array set c {0 0 1 0}} {$i < 1000000} {incr i} {

incr c([unbiased $biased])

   }
   puts [format "unbiased %d => #0=%d #1=%d ratio=%.2f%%" $n $c(0) $c(1) \

[expr {100.*$c(1)/$i}]] }</lang> Sample output:

  biased 3 => #0=667076 #1=332924 ratio=33.29%
unbiased 3 => #0=500263 #1=499737 ratio=49.97%
  biased 4 => #0=750470 #1=249530 ratio=24.95%
unbiased 4 => #0=500644 #1=499356 ratio=49.94%
  biased 5 => #0=800243 #1=199757 ratio=19.98%
unbiased 5 => #0=500878 #1=499122 ratio=49.91%
  biased 6 => #0=833623 #1=166377 ratio=16.64%
unbiased 6 => #0=500518 #1=499482 ratio=49.95%