00:01
In this exercise, we are told that patients who come into the hospital with heart failure, in 87 % of the instances, the heart failure is due to natural occurrences, and in 13 % of the instances, the heart failure is due to outside factors.
00:19
And now we have parts a, b, and c, and these three parts ask questions in terms of the number of patients who have to come into the emergency until we find a patient who has heart failure due to outside factors.
00:34
So that is the number of patients with heart failure who come into the emergency until we find one, until we find the first one, that has heart failure due to outside factors rather than natural occurrences.
00:47
So let's label heart failure due to outside factors as p.
00:55
And x is the number of patients arriving at the emergency with heart failure until we find the first one which has heart failure due to outside factors.
01:31
And so based on this, x is a geometric random variable.
01:39
So for a, what is the probability that the first patient with heart failure who enters the emergency room has the heart failure condition due to outside factors? so that is the probability that the number of trials is one until we find the first one who has heart failure due to outside factors.
02:01
And the formula for this probability simplifies to p.
02:07
So you have a 13 % chance.
02:10
The first one has heart failure due to outside factors.
02:15
And for part b, we are asked for the probability that the third heart failure patient who enters the emergency room is the first one that has heart failure due to outside factors...