Online executable Python solution to the Tuesday boy problem

Online executable Python solution to the Tuesday boy problem(ideone.com)

2 points by daivd 12 years ago | 10 comments

x0054 12 years ago |

This answer is incorrect. There is a 1/4 chance that both children are boys, and each child has 1/2 chance of being borne a boy, regardless of what day his sibling was or will be borne on. The program arrives at the probability of 13/27 by excluding the possibility that both children might be borne on tuesday and both might be boys.

daivd 12 years ago | |

No, it does not exclude that possibility (print the final list of pairs if you want to check). The calculation is correct. The result is counter-intuitive to almost everyone, which is why I made the program, so you can convince yourself.

x0054 12 years ago | | |

Nope, sorry, it's wrong. Here are the possibilities for someone with 2 children were at least one of them is a boy borne on tuesday:

  01) 1BT 2BM
  02) 1BT 2BT
  03) 1BT 2BW
  04) 1BT 2BR
  05) 1BT 2BF
  06) 1BT 2BS
  07) 1BT 2BY
  
  08) 1BT 2GM
  09) 1BT 2GT
  10) 1BT 2GW
  11) 1BT 2GR
  12) 1BT 2GF
  13) 1BT 2GS
  14) 1BT 2GY
  
  15) 1BM 2BT
  16) 1BT 2BT
  17) 1BW 2BT
  18) 1BR 2BT
  19) 1BF 2BT
  20) 1BS 2BT
  21) 1BY 2BT 
  
  22) 1GM 2BT
  23) 1GT 2BT
  24) 1GW 2BT
  25) 1GR 2BT
  26) 1GF 2BT
  27) 1GS 2BT
  28) 1GY 2BT

Your program counts possibility # 2 and 16 only once, because at first glance they are identical. But they are not, because each child has independent probability. This is why models that graph this information on a grid also fail to get the right answer. The above probability table gives you the proper result of 14/28, or 1/2.

01) 1BT 2BM 02) 1BT 2BT 03) 1BT 2BW 04) 1BT 2BR 05) 1BT 2BF 06) 1BT 2BS 07) 1BT 2BY 08) 1BT 2GM 09) 1BT 2GT 10) 1BT 2GW 11) 1BT 2GR 12) 1BT 2GF 13) 1BT 2GS 14) 1BT 2GY 15) 1BM 2BT 16) 1BT 2BT 17) 1BW 2BT 18) 1BR 2BT 19) 1BF 2BT 20) 1BS 2BT 21) 1BY 2BT 22) 1GM 2BT 23) 1GT 2BT 24) 1GW 2BT 25) 1GR 2BT 26) 1GF 2BT 27) 1GS 2BT 28) 1GY 2BT

girl = 0 boy = 0 do 10000 times { child1Sex = randomSex; child1Day = randomDay; child2Sex = randomSex; child2Day = randomDay; if ( (child1Sex == "B" AND child1Day == "Tu") OR (child2Sex == "B" AND child2Day == "Tu") ) { if (child1Sex == child2Sex){ boy++ } else { girl++ } } } print "Ratio of boys and girls is " + boy " : " + girl;