Probability & Odds
Chance is full of surprises. Play with these experiments β roll dice, flip coins, open doors β and watch your gut instinct get proven wrong, then see the real math behind the luck.
How many people need to be in a room before two of them probably share a birthday? Way fewer than you'd guess.
In a room of 23, there's a 50.7% chance at least two people share a birthday. At just 23 people it's already better than a coin flip!
A car hides behind one of three doors; goats behind the other two. Pick a door. The host opens a different door showing a goat. Should you stay, or switch?
Switching wins about 2 out of 3 times β because your first pick is only right 1/3 of the time, so the car is behind the other door twice as often.
Roll real dice and watch your results stack up into the exact shape the math predicts. One die is flat; add dice and the middle bulges.
A 7 on two dice has six ways to happen (1-6, 2-5, 3-4β¦) but a 2 has only one β so 7 comes up six times as often. Keep rolling and your bars climb to meet the outline.
Each flip is 50/50, but small runs look lopsided (three heads in a row is common!). Flip a thousand and both bars settle onto the dashed halfway line β the law of large numbers at work.
| Flip heads on a coin | 1 in 2 |
| Roll a 6 on one die | 1 in 6 |
| Roll two 6s at once | 1 in 36 |
| Be born on a leap day | 1 in 1,461 |
| Get a royal flush (poker) | 1 in 649,740 |
| Struck by lightning this year | 1 in ~1.2 million |
| Win a 6/49 lottery jackpot | 1 in 13,983,816 |
"Odds" and "probability" aren't the same thing: a 25% chance is 1 in 4 as a probability, but 3 : 1 against as odds (three ways to lose for each way to win).
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