Everybody seems to have gone home last night and tried my June Diary brainteaser. There’s much incredulity from readers that the answer could possibly be anything other than 1/2. Well, it can. The answer is 13/27. Here’s the problem as stated:

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?

With “B” for “boy” and “G” for “girl,” and days of the week abbreviated in an obvious way, I have told you that my particular two-child family belongs to a certain subset of all possible two-child families. Here is the actual subset. The left-hand column is the first-born child, the right-hand column is the second-born. B-Tu B-Mo B-Tu B-Tu B-Tu B-We B-Tu B-Th B-Tu B-Fr B-Tu B-Sa B-Tu B-Su B-Tu G-Mo B-Tu G-Tu B-Tu G-We B-Tu G-Th B-Tu G-Fr B-Tu G-Sa B-Tu G-Su B-Mo B-Tu B-We B-Tu B-Th B-Tu B-Fr B-Tu B-Sa B-Tu B-Su B-Tu G-Mo B-Tu G-Tu B-Tu G-We B-Tu G-Th B-Tu G-Fr B-Tu G-Sa B-Tu G-Su B-Tu These all occur with equal probability. That’s why birth order matters. If I toss a fair coin twice, I can get HH, HT, TH, or TT with equal probability 1/4 each. If you ignore order and ask “What’s the chance of a head and a tail in any order?” the answer is 1/2. You lost the equal probability. Of these 27 possibilities, each occurring with equal probability, 13 have two boys. Q.E.D. [That’s a “front” presentation. If you want to see my actual thought processes in all their grubby chaos, they are here.]