Skill: probability

Probability Lab

Apply the addition and multiplication rules, tell independent from dependent events, and count with permutations and combinations.

1 Law of large numbers lab

Flip a fair coin and track the proportion of heads. Short runs swing wildly; long runs settle near 0.5.

The chart plots P(heads) after each flip. Watch it home in on the dashed 0.5 line.

Flips: –

Heads: –

Proportion: –

After 10 flips, 0.7 heads is ordinary luck — after 1000 flips it would be shocking.
The law of large numbers: the observed proportion converges to the true probability as trials grow.
Streaks (HHHHH) happen in fair coins too — randomness has no memory, so the next flip is still 50/50.