# State the overall health question you have been asked to address in your own words. Be sure you capture the key elements of the question, using language that a non-technical audience can understand. Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog.

- State the overall health question you have been asked to address in your own words. Be sure you capture the key elements of the question, using language that a non-technical audience can understand.
- Let A represent cat ownership and B represent dog ownership. Suppose 35% of households in a population own cats, 30% own dogs, and 15% own both a cat and a dog. Suppose you know that a household owns a cat. What is the probability that it also owns a dog?

Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.

If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?

If we randomly select two women from the population who then become pregnant, what is the probability that the first woman’s child will be a boy and the second woman’s child will be a boy?

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If we randomly select two women from the population who then become pregnant, what is the probability that both children will be boys given that at least one child is a boy?

Explain the difference between mutually exclusive and independent events.

Suppose a screening test has a sensitivity of 0.80 and a false-positive rate of 0.02. The test is used on a population that has a disease prevalence of 0.007. Find the probability of having the disease given a positive test result.