Mon Prof Augmenté
Bouncing Balls on Pegs
Age 18 · Maths
A binomial distribution B(n, p) counts successes in n independent trials, each with success probability p. Its expected value is np and its variance is np(1-p).
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In the picture
- Top brass peg: the first left-or-right bounce point
- Steel ball at the peg: one independent trial with two outcomes
- Vertical slot at the bottom: one possible total number of successes
- Tallest middle pile: the most likely total, close to np
- Shorter side pile: a total farther from np, showing spread
Examples
- Flipping a coin ten times and counting heads
- Taking ten free throws and counting baskets
Key takeaways
- For B(n, p), the expected number of successes is np.
- The variance is np(1-p), so the standard deviation is sqrt(np(1-p)).
Quiz: Bouncing Balls on Pegs (Age 18)
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In the notation B(n, p), what does p represent?
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For a binomial distribution B(n, p), what is the expected number of successes?
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For a binomial distribution B(n, p), what is the variance?
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