Boy or Girl Paradox Calculator
Boy or Girl Paradox: Q1 gives 1/2, Q2 gives 1/3. How you ask changes the answer. Interactive sample
Why This Statistical Analysis Matters
Why: Statistical calculator for analysis.
How: Enter inputs and compute results.
Boy or Girl Paradox — 1/2 vs 1/3
Same family, two children. "Older is a boy" → 1/2. "At least one is a boy" → 1/3. The difference comes from HOW the information is obtained.
Examples — Click to Load
Question Mode
Sample Space
| Child 2: Boy | Child 2: Girl | |
|---|---|---|
| Child 1: Boy | BB | BG |
| Child 1: Girl | GB | GG |
Inputs
Calculation Breakdown
Q1 vs Q2 Comparison
Sample Space Doughnut
⚠️For educational and informational purposes only. Verify with a qualified professional.
Key Takeaways
- • Same family, different probabilities — how you ask changes the answer
- • "Older child is a boy" → P(both boys) = 1/2 (you specified which child)
- • "At least one is a boy" → P(both boys) = 1/3 (you didn't specify which)
- • Tuesday Boy variant: "One is a boy born Tuesday" → P(both boys) = 13/27 ≈ 0.481
Did You Know?
How It Works
1. Sample Space
Four equally likely outcomes: {BB, BG, GB, GG}. Child 1 = older, Child 2 = younger.
2. Q1: Older is Boy
Eliminates GG and GB. Remaining {BB, BG}. P(both boys) = 1/2.
3. Q2: At Least One Boy
Eliminates only GG. Remaining {BB, BG, GB}. P(both boys) = 1/3.
4. Why Different
Information specificity changes the conditional probability. Specifying WHICH child narrows the space differently.
Comparison: Q1 vs Q2 vs Tuesday Boy
| Variant | Condition | P(both boys) |
|---|---|---|
| Q1: Older is Boy | Specified which child | 1/2 |
| Q2: At Least One Boy | Unspecified which | 1/3 |
| Tuesday Boy | At least one boy born Tuesday | 13/27 ≈ 0.481 |
Frequently Asked Questions
Why do Q1 and Q2 give different answers?
Q1 specifies WHICH child (older), eliminating half the sample space. Q2 only tells you 'at least one' is a boy, eliminating only GG. The process of learning matters.
What is the Tuesday Boy variant?
Gary Foshee (2010): 'One is a boy born on a Tuesday.' This seemingly irrelevant detail changes the sample space. With 14×14 possibilities, the answer becomes 13/27.
By the Numbers
Official Sources
Disclaimer: Educational purposes. Theoretical results (1/2 and 1/3 for p=0.5) are mathematically rigorous. Simulations subject to random variation.