Binomial and Poisson distributions
Count the paths of a tree that give exactly k successes, see where the binomial formula comes from, and use the Poisson formula for events that arrive at random.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- UK: Year 13
- France: grade 11
- Germany: grade 12
- Afghanistan: grade 12
- Syria: grade 12
- Palestine: grade 11
- Russia: grade 10
Guide
This studio follows Afghan grade 12 chapter 7 (Bernoulli trials and the binomial distribution, the Poisson distribution) and the UK A-level B(n, p).
In n independent trials, each with the same probability p of success, the probability of exactly k successes is (number of paths with k successes) × pk×(1 − p)n − k. The Poisson distribution counts events that happen at random in time or space, with average λ: P(X = k) = e−λ×λk ÷ k!.
Common mistakes worked on here: using only one path, using 12 for a bent coin, forgetting the number of paths, and answering with e−λ alone.