Answer:
a) 11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.
b) 0.0871 = 8.71% probability that third patient with heart failure that enters the emergency room is the first one due to outside factors.
c) The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.
Step-by-step explanation:
We have these following probabilities:
89% probability that a patient has heart failure due to natural occurrences.
11% probability that a patient has heart failure due to outside factors.
A) What is the probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors?
We assume that causes of heart failure between individuals are independent, which means that the probabilities are the same for each patient. So:
11% probability that the first patient with heart failure that enters the emergency room has the conditions due to outside factors.
B) What is the probability that third patient with heart failure that enters the emergency room is the first one due to outside factors?
First two due to natural occurrences, each with 89% = 0.89 probability.
Third due to outside factors, with 11% = 0.11 probability. So
0.89*0.89*0.11 = 0.0871
0.0871 = 8.71% probability that third patient with heart failure that enters the emergency room is the first one due to outside factors.
C) What is the mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors?
11% with outside factors, so the mean number of patients before the first with outside factors is given by
m = 1/0.11 = 9.09
The mean number of heart failure patients with the condition due to natural causes that enter the emergency room before the first patient with heart failure from outside factors is 9.09.
=a known y coordinate & 
=a known x coordinate.