Could It
Be Chance?
There are 30 children in a class. What is the chance that at least two of them share the same birthday?
(a) Very small (b) About half (c) More likely than not
Make your guess before you read on.
💡 The Idea
Most people guess that the chance is tiny: after all, there are 365 days in a year. But the answer is (c). In a class of just 23 children, the chance of a shared birthday is a little more than half. In a class of 30, it’s about 70 in 100.
How can that be? You aren’t looking for someone who shares your birthday. Any two children can match, and in a class of 30 there are 435 different pairs of children. With so many chances, a match is likely.
This is the secret of coincidences. Any one particular coincidence is unlikely. But there are so many chances for some coincidence to happen that surprising things happen all the time.
Right by chance
If you guess which of two cups hides a coin, you’ll be right about 5 times out of 10. But chance goes up and down. Now and then, someone will get 8 or 9 right, just by chance. That’s why one good score proves nothing. A real power would keep scoring high, test after test.
The phone call coincidence
You think of a friend, and the phone rings: it’s her! Amazing? Think how many times you’ve thought of friends who didn’t call, and how many calls came when you weren’t thinking of the caller. You don’t remember those. With millions of people thinking and phoning every day, coincidences like this must happen to someone, somewhere, every day.
Before calling it a miracle, ask:
how often would this happen just by chance?
🔗 Where You’ve Seen It
- Activity 2: The Pendulum That Knows the Answer
In the coin test, guessing gets you about 5 out of 10. The pendulum did no better than guessing. - Activity 8: The “Mid-Brain” Mystery
If a blindfolded reader just guesses the colour of a card from four colours, they’ll be right about one time in four. A fair test needs many cards, not one guess that happens to be right.
🌍 Use It Everywhere
If a fortune-teller makes a hundred predictions, a few will “come true” just by chance, and those are the ones people remember. A lottery winner may say their “lucky number” worked, but someone had to win, and many other people with “lucky” numbers lost.
Toss a coin 10 times, and before each toss, guess “heads” or “tails”. Count how many you got right. If everyone in a class of 30 does this, one or two children will probably get 8 or more right, just by chance!
Would it be fair to call those children psychic? What should they do next?
Show the answer
No. They should test again! A winning streak that comes from chance doesn’t last. Next time, the “winners” will usually score about 5 out of 10, like everyone else. A real power would keep winning.
For parents and teachers
- The birthday problem: the probability that at least two of n people share a birthday passes 50% at n = 23 and is about 70% at n = 30 (ignoring leap years). See “Using Probability to Understand the Birthday Paradox” (Scientific American), which includes a classroom activity.
- The coin numbers: the chance of 8 or more correct guesses out of 10 is 56 in 1,024, about 5.5%. In a class of 30, the chance that at least one child does this is about 80%.
- Going further: older children can explore why a high score that came by chance tends to be followed by an ordinary one, an effect statisticians call “regression to the mean”.
A Young Skeptics thinking tool, written with the assistance of AI tools, and reviewed by our editors. — CHARVAKA DESK