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.
