Question: A recent study in the Journal of the American Medical Association (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after 11 pm. The study investigated 58,593 cardiac arrests that occurred during the day or evening. Of those, 11,604 survived to leave the hospital. There were 28,155 cardiac arrests during the shift that began at 11 pm, commonly referred to as the graveyard shift. Of those, 4,139 survived for discharge. The following contingency table summarizes the results of the study.
a. What is the probability that a randomly selected patient experienced cardiac arrest during the graveyard shift?
b. What is the probability that a randomly selected patient survived for discharge?
c. Given that a randomly selected patient experienced cardiac arrest during the graveyard shift, what is the probability the patient survived for discharge?
d. Given that a randomly selected patient survived for discharge, what is the probability the patient experienced cardiac arrest during the graveyard shift?
e. Is whether or not a patient survives independent of the timing of the cardiac arrest? Explain using probabilities. Given your answer, what type of recommendations might you give to hospitals?