🧠 Why Question B Trips People Up
In Question B, knowing "at least one is a boy" doesn't tell us WHICH one. The sample space isn't {BB, BG} but {BB, BG, GB}. Boy-Girl and Girl-Boy are DIFFERENT outcomes! Only 1 of 3 is Boy-Boy, so P = 1/3.
🔑 The Key Insight
The answer depends on HOW you learned the information. Did you meet a specific child who happens to be a boy? Or did you learn abstractly that "at least one" is a boy? The mechanism of revelation changes the probability!
Question A: "Older is Girl"
Question B: "At Least One Boy"
Tuesday: "Boy Born on Tuesday"
Adding "born on Tuesday" seems irrelevant, but it changes everything!
BB cases with Tuesday boy: 13
(7 where first is Tue-Boy + 7 where second is Tue-Boy - 1 overlap)
BG/GB cases with Tuesday boy: 14
(7 for BG + 7 for GB)
📜 Martin Gardner (1959)
This paradox first appeared in Gardner's "Mathematical Games" column in Scientific American. It sparked intense debate among readers and has been confusing people ever since. The "Tuesday Boy" variant was added later by Gary Foshee at a 2010 puzzle conference, creating even more confusion about how seemingly irrelevant information changes probabilities.