Section 2.4: Binomial Distribution

Bernoulli trials and counting successes

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The Free-Throw Challenge

🏀 A Basketball Story

Imagine a basketball player who makes 70% of their free throws. They step up to shoot 10 free throws in a row.

Here's what we want to know:

  • • What's the probability they make exactly 7 shots?
  • • What's the probability they make at least 8?
  • • On average, how many will they make?

This is the Binomial Distribution!

Whenever you have a fixed number of independent trials, each with the same success probability, and you're counting successes — that's the Binomial Distribution.

n = 10

Number of trials (shots)

p = 0.70

Success probability

Real-world examples: Coin flips, quality control (defective items), medical trials (patients who respond), survey responses (yes/no), exam questions (correct/wrong)...