Let the coins decide.
The experiment
Ready?
Penny
?
Dime
Your next flip starts here.
Given at least one head
Both are heads
—%
0 HH ÷ 0 eligible flips
Theory 33.33%Waiting for flips
Given at least one tail
Both are tails
—%
0 TT ÷ 0 eligible flips
Theory 33.33%Waiting for flips
Probability, as it happens
Both headsBoth tails┄ Theory: 33⅓%
First flip0 total flips
Every flip, on record · 0
Newest first · H = heads, T = tails · percentages are cumulative
| Flip | Run | Time | Penny | Dime | Outcome | HH | ≥1 H | TT | ≥1 T |
|---|
No flips yet
Why should this approach ⅓?
HH, HT, TH, and TT are equally likely. “At least one head” excludes TT, leaving three outcomes. Only HH has two heads: 1 out of 3. For tails, exclude HH instead. Again, 1 out of 3.
Where does ½ come from?
If you know the penny specifically is heads, only HH and HT remain. The dime is heads in 1 out of 2. That is different information from “at least one coin is heads.” Small samples fluctuate; more flips tend toward the theoretical values.