Probability: Predicting the Unpredictable
What are the chances?
What are the chances?
Click Flip to flip coins. Watch the running percentage of heads. With few flips, it jumps around. With many, it settles toward 50%. This is the law of large numbers in action.
Roll two dice and add them. Some totals (like 7) are much more likely than others (like 2 or 12). Roll many times and the distribution emerges. Click to roll.
You use probability every day, often without realizing it.
"30% chance of rain" means: in 100 days with these conditions, it rained 30 times. It does not mean 30% of the area will get rain.
Game designers use probability to balance loot drops, critical hits, and spawn rates. A "1% legendary drop" means you need about 100 tries on average.
A basketball player shooting 40% from three-point range will miss most shots. But over a season, their percentage is remarkably consistent.
The "Birthday Paradox": in a group of just 23 people, there is a 50% chance two share a birthday. With 70 people, it is 99.9%. Our intuition about probability is often wrong because we underestimate combinations.
You've discovered that randomness has rules. Individual events are unpredictable, but patterns emerge over many trials. Probability is the math of uncertainty, and it governs everything from weather forecasts to game design.
The chance of an event = favorable outcomes / total outcomes. A coin has 1 heads out of 2 sides = 50%. A die has 1 six out of 6 faces = 16.7%.
Flip a coin 10 times and you might get 8 heads. That does not mean the coin is unfair. Small samples are noisy. Patterns need many trials to emerge.
As you flip more coins, the percentage of heads gets closer to 50%. With 10 flips it varies wildly. With 10,000 it barely budges from 50%.
A coin has no memory. Getting 5 heads in a row does not make tails "due." Each flip is independent. Past results do not change future odds.
Put your new knowledge into practice!