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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)...