Practice - Derivation Idea
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Practice Questions
Test your understanding with targeted questions
What does the binomial distribution model?
💡 Hint: Consider what outcomes are being counted.
Explain what is meant by 'choosing k successes.'
💡 Hint: Think about how many sequences can be formed.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is (n choose k)?
💡 Hint: Think of it as counting ways to pick items.
The binomial distribution can only be used if trials are independent.
💡 Hint: Consider the definition of independent trials.
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Challenge Problems
Push your limits with advanced challenges
A factory produces 100 lightbulbs, and there's a 5% chance any bulb is defective. What’s the probability that exactly 3 bulbs are defective?
💡 Hint: Break the calculation into the binomial coefficient and separate terms for success and failure.
In a game, you roll a die 30 times and win by rolling a 4 (p = 1/6). What’s the probability of rolling exactly 5 fours?
💡 Hint: Calculate the combinations and the probabilities separately to build the answer.
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Reference links
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