In a study of outcomes for patients who had been in the Intensive care Unit (ICU) at a large hospital, the records from last 150 patients who had been in the ICU for more than one day are obtained. The data for the number of patients in four categories is summarized in the table below.

So of the 150 patients, 120 were diagnosed with Coronary Heart Disease (CHD), 52 had both CHD and stroke, 68 had CHD but not stroke, etc. A patient record is selected at random. Let A be the event that the record is for an ICU patient who had CHD, and B be the event that the record is for a patient who had a stroke.

a) i) Are the events A and B independent? Explain.

ii) Are the events A and B mutually exclusive? Explain.

iii) Find P (AB).

iv) Find P (A υB).

b) For a detailed chart review, 50 of the 150 records are selected at random without replacement.

i) Find the probability that the sample contains 45 patients with CHD. (An expression is OK here, but tries to do the calculation).

ii) Find the probability that the sample contains more than 45 patients with CHD or stroke. (An expression is OK here, but tries to do the calculation).