Question

The probability a patient in a U.S. hospital was in a California hospital is 0.12. The probability a patient in a U.S. hospital had a hospital stay of fewer than four days is 0.6. Assume whether a patient in a U.S. hospital was in a California hospital is independent of whether the person has a hospital stay of fewer than four days.

What is the probability a person in a U.S. hospital was in a California hospital given the hospital stay was fewer than four days?

a. 0

b. 0.12

c. 0.2

d. 0.48

e. 0.6

Answer 1

Since, we have assumed that the events "patient was in a California hospital" and "hospital stay of fewer than four days" are independent

=> the probability a person in U.S. hospital was in a Californial hospital given the hospital stay was fewer than four days = the probability a patient in a U.S. hospital was in a California hospital

(Since, the two events are independent, the occurence of the event "hospital stay of fewer than four days" does not affect the probability of the event "patient was in a California hospital")

Hence,

the probability a person in U.S. hospital was in a Californial hospital given the hospital stay was fewer than four days = 0.12

Thus, the correct option is OPTION b. 0.12

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