00:01
Here we have three patients that are accepted into a clinical trial for a new drug.
00:06
And it's been estimated that the probability that the drug is effective for patient a is 0 .7.
00:14
So we will call event a, the event in which the drug is effective for patient a.
00:19
And the same goes for b and c.
00:21
The probability that the drug is effective for patient b is 0 .2, and it's 0 .6 for patient c.
00:29
We're also told to assume that the success of the drug for the three patients is independent, which means that the outcome for one patient has no bearing on the other two patients and vice versa.
00:41
And we are asked to draw a t diagram displaying all the outcomes and joint probabilities measuring the effectiveness of the drug for all three patients.
00:51
So we can make three generations of branches in this tree, one generation for b, one for a and one for c.
00:59
So let's say the first generation of branches is whether the drug is effective for patient a or not.
01:11
Actually, we can write it like this.
01:13
A means it's effective for patient a, and a prime means it's not effective for patient a.
01:24
And then for patient b, if it's effective for patient a, it may be effective for patient b, or it might not.
01:43
And then if it's successful for patient b, it may or may not be successful for patient c.
02:01
And so for this branch, the outcome is a, b, and c.
02:09
For this branch, the outcome is a, b, and c prime, and so on.
02:25
So this is all of the possible outcomes.
02:28
And we can also add the probabilities for each individual branch...