Drag rhythmic values into up to 8 beat blocks per line to build a drum groove, or click a tile then click a block to place it — handy on a trackpad.

🎵 Probability Lesson 11: Expected All-Failure Groups — Compute N × f^k for Repeated Independent Failures mess around all you want, nothing here saves
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Probability, Lesson 11: Expected All-Failure Groups

Math skill: Compute N × f^k for Repeated Independent Failures

How the beat teaches it: Every slot gives N independent groups of k trials each, with a per-trial failure probability f — the expected number of groups with zero successes is N times f raised to the k. Build that many notes anywhere in the kit.

This is lesson 11 of 24 in RockBlocks Math, Probability, a free course where every lesson turns a math idea into something you can count, hear, and play. The previous lesson, Mean of a Geometric Distribution,” covered compute E[X] = 1/p. Next is Lesson 12, Mean of a Poisson Distribution.”

Every slot above (A, B, C, D) is its own question, and it’s a real, blank RockBlocks beat the whole time — the same drag-and-drop tiles, kit, tempo, sheet music, and drummer view as anywhere else on the site. Tap ❓ Questionin the corner to read the current slot’s problem, build your answer right in the grid, then tap ✓ Check Answerto grade it. Once you’re done, keep going: expand the beat, drop it into a Stack, or save a copy to your own page — nothing here overwrites the lesson itself, so every visitor still starts from the same blank slots.