Practice Derivation Of Bayes’ Theorem (5.X.3) - Bayes’ Theorem - Mathematics - iii (Differential Calculus) - Vol 3

Practice: Derivation of Bayes’ Theorem

Lesson 5.X.3Bayes’ Theorem

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9 questions

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6 sample questions

Question 1.
Define sample space.
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Think of what you would observe.
Question 2.
What does conditional probability measure?
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It involves two events.
3Question 3.
What is Bayes' Theorem used for?
- To derive frequency distributions
- To update probabilities based on new data
- To calculate means and variances
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Think about updating beliefs.
4Question 4.
True or False: The prior probability changes when new evidence is introduced.
- True
- False
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What does 'prior' mean?
Question 5.
A factory produces 5% defective items. An inspection process has an 80% success rate in detecting defects. If an item is inspected and found defective, what is the probability that it is actually defective?
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Work through joint probabilities and apply Bayes' Theorem carefully.
Question 6.
In clinical trials, a new drug shows efficacy in 70% of patients. There is a 10% chance of side effects. If side effects occur, what's the updated probability that the patient benefited from the drug?
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Set up your known probabilities and use Bayes' formula.

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