World Cup Math: Birthday Paradox

Source: http://www.bbc.com/news/magazine-27835311

It’s puzzling but true that in any group of 23 people there is a 50% chance that two share a birthday. At the World Cup in Brazil there are 32 squads, each of 23 people… so do they demonstrate the truth of this mathematical axiom?

Imagine the scene at the Brazilian football team’s hotel. Hulk and Paulinho are relaxing after another stylish win. Talk turns from tactics to post World Cup plans.

“It’ll be one party after another,” says Hulk, confidently assuming Brazilian victory on home soil. “First the World Cup, then my birthday a couple of weeks later.”

“Your birthday’s in July?” replies Paulinho. “Me too – 25 July, when’s yours?

“No way, exactly the same day!” exclaims Hulk incredulously. “What are the chances of that?”

With 365 days in a regular year, most people’s intuitive answer would probably be: “Pretty small.”

But in this case our intuition is wrong – and the proof of that is known as the birthday paradox.

Hulk and Paulinho