In a recent article U.S. News and World Report rated pediatric hospitals and provided data on several characteristics, including daily inpatient volume and nursetopatient ratio, for the top 30 hospitals on its list (U.S. News and World Report, June 9, 2008). Suppose we consider a daily inpatient volume of at least 200 to be high and a nursetopatient ratio of at least 3.0 to be high. Sixteen hospitals had a daily inpatient volume of at least 200, one third of the hospitals had a nursetopatient ratio of at least 3.0, and seven of the hospitals had both a daily inpatient volume of at least 200 and a nursetopatient ratio of at least 3.0.
a. Find the probability of a hospital having a daily inpatient volume of at least 200, the probability of a hospital having a nursetopatient ratio of at least 3.0, and the probability of a hospital having both a daily inpatient volume of at least 200 and a nursetopatient ratio of at least 3.0.
b. What is the probability that a hospital had a daily inpatient volume of at least 200 or a nursetopatient ratio of at least 3.0 or both?
c. What is the probability that a hospital had neither a daily inpatient volume of at least 200 nor a nursetopatient ratio of at least 3.0?
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