(a)
Let us define the following events:
Surgery performed at “high-volume hospital”
Surgery performed at “low-volume hospital”
A patient died.
A patient survived.
From the data,
P [Patient is alive after surgery at “high-volume hospital”]
P [Patient has surgery at “high volume” hospital and survived]
.
The probability that a patient has surgery at “High volume Hospital” and survived is 0.76.
(b)
Let E be the event that a randomly chosen patient survives the first two weeks after surgery.
The probability that a randomly chosen patient survives is 0.98.
(c)
P (A randomly chosen patient dies)
.
Let A be the event that a patient dies and B be the event that a patient survives.
P [out of two patients, one survives]
Probability that out of two patients, one survives is 0.0196.
(d) P [At least one survives]
The probability that at least one patient survives is 0.99.