Chap 2 Probability Student.pdf

2 whats the probability that a randomly selected

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2. What’s the probability that a randomly selected student from the class is sophomore given they’re a male? 3. What’s the probability that a randomly selected student from the class is male given they’re a sophomore? Example : The probability that Sam parks in a no-parking zone and gets a parking ticket is 0.06, and the probability that Sam cannot find a legal parking spot and has to park in the no-parking zone is 0.20. On Tuesday, Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket. Law of Total Probability : Let be mutually exclusive and exhaustive events and be any event.
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Bayes Theorem : Let be mutually exclusive and exhaustive events with prior probabilities and be any event for which Then, the posterior probability of given has occurred is given by: Example : A blood test is 99% effective at detecting a certain disease if, in fact, the disease is present. The test also yields a positive result for 1% of the healthy individuals tested. Suppose the disease is quite rare; only 0.5% of the population actually has the disease. If an individual has a positive test what is the probability they actually have the disease?
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Note : The Multiplication Rule can be found by taking the conditional probability formula and multiplying both sides by the marginal probability in the denominator. That is, Example :
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