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Which of the following wordings should you interpret as a conditional probability question?
In a study of 500 households, 75 households both own a dog and subscribe to a home delivery service. What is the joint probability a randomly chosen household both owns a dog and subscribes to a delivery service? Provide the simplified fraction and decimal.
A college tracks the number of male and female students who graduate with degrees in science and non-science fields:
What is the probability that a randomly selected science graduate is male?
A university study reports the following: of students who complete a tutoring program pass the final exam, of students who complete the tutoring program and attend all review sessions pass the final exam, and of students who complete the tutoring program, attend all review sessions, and submit all assignments pass the final exam. Which expression correctly represents the statement ' of students who complete the tutoring program and attend all review sessions pass the final exam' as a conditional probability?
Two boxes are used: Box 1 contains 3 red and 2 blue marbles, Box 2 contains 1 red and 4 blue marbles. A box is chosen with probabilities 0.6 for Box 1 and 0.4 for Box 2. A marble drawn is red. What is the probability it came from Box 1?
A disease has prevalence 1% in a population. A diagnostic test has sensitivity 95% (P(test+|disease)=0.95) and specificity 90% (P(test-|no disease)=0.90). If a randomly chosen individual tests positive, what is the probability they actually have the disease?