References: Counts and trials: the binomial distribution

Source material

Source curriculum (structural mirror, cited as further study):
• Khan Academy, "Random variables" (binomial distribution, Statistics & Probability)
  Author: Sal Khan and the Khan Academy team
  Unit page: https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library
  License: CC BY-NC-SA 4.0
Clawdemy's lessons are original prose that follows the pedagogical arc of this
unit. We do not embed, reproduce, or transcribe Khan's text or videos; we link
out to the relevant unit as recommended further study. The non-commercial
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Source-scope note: this lesson mirrors Khan's binomial material (the binomial
setting, the probability formula, the n-times-p expected value) and restates it
in Clawdemy's voice with original examples (coins, a model's accuracy, API
calls). The counting factor C(n, k) is introduced lightly; Khan's "Counting,
permutations, and combinations" unit is the fuller treatment. The AI framing
(accuracy as a binomial count, conversion rates, the large-n normal
approximation as a CLT preview) is Clawdemy framing. Exact per-unit URLs are
verified at promotion.

Read this next

• Khan Academy: Random variables (binomial distribution) by Sal Khan and the Khan Academy team. The unit this lesson mirrors, with videos and practice on Bernoulli and binomial random variables, the probability formula, and the mean and variance, free and CC-licensed. The place to drill exactly-k and at-least computations.

Going deeper

A short, durable list. Both are free.

• Khan Academy, “Counting, permutations, and combinations” (within the course above). The fuller story behind C(n, k): how to count arrangements, which this lesson uses but only introduces. Worth a pass if the combinations factor feels mysterious.
• Khan Academy, “Sampling distributions” (within the course above). The bridge to the next phase: as the number of trials grows, the binomial approaches the normal, and sample counts and proportions become approximately normal, which is the central limit theorem.

Adjacent topics

Where this sits inside this track.

• Random variables and expected value. The earlier Phase 3 lesson. The binomial is a specific random variable, and its n-times-p expected value is the expected-value idea specialized to counting.
• The bell curve: the normal distribution. The previous lesson. For large n the binomial smooths into the normal; the two distributions meet there.
• From sample to population: sampling and the central limit theorem. The next lesson and the start of Phase 4. It explains why sums and counts like the binomial tend toward the normal, and why that makes inference possible.