The long night of coin flips
Flip a fair coin ten times and you might get 7 heads, but flip it ten thousand times and heads settles near half. Probability isn't a promise about the next flip — it's what the long run reliably averages out to.
How likely is it?
Probability is the number of favorable outcomes divided by the total number of equally-likely outcomes. Rolling a single die, P(4) = 1/6. With two dice, some sums are more likely because there are more ways to make them.
Simulation · Two-dice probability
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7 is the most likely sum — there are more ways to make it.
Roll two dice many times. The bars climb toward a peak at 7 — the most probable sum.
Lab · Why 7?
- List the dice pairs that sum to 7 (1+6, 2+5, 3+4, …).
- List the pairs that sum to 2 (just 1+1).
- Roll ×100 a few times and watch the shape.
What you should see: There are six ways to make 7 but only one to make 2, so 7 is six times as likely.