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Which of the following is the correct formal definition of the conditional probability P(B|A)?
A survey of drivers recorded whether each driver texted while driving and whether they received a warning last year. The counts from the survey show that drivers both texted while driving and received a warning, and drivers received a warning in total. What is the probability that a driver texts while driving, given that they received a warning last year?
A certain disease is present in of a population. A screening test for the disease is positive of the time when the person has the disease and of the time when the person does not have the disease. Let be the event "the person has the disease" and be the event "the test is positive." What is the probability that a person actually has the disease given that they test positive?
Bag L contains 4 red and 6 blue marbles; Bag R contains 5 red and 15 blue marbles. A bag is selected with P(L)=2/3 and P(R)=1/3. A drawn marble is red. What is the exact probability it came from Bag L (simplified fraction)?
Algebraically derive Bayes' theorem starting from the conditional probability identity and . Which equation correctly shows the derivation of Bayes' formula?