00:01
Make a little tree diagram of what's happening.
00:02
These are actuarial tests, and the probability that she passes the first test is 0 .9, so the probability she fails the first test is 0 .1.
00:11
And then if she passes the first test, the likelihood of passing the second test is 0 .8, and the probability that she fails at is 0 .2.
00:22
And then if she passes both of those, the probability she passes this third one is 0 .7, and then the probability she fails at is 0 .3.
00:33
So we want to find in part a, what is the probability that she passes all three? so three passes.
00:40
And that's going to be following along this first branch of the tree.
00:44
That's going to be the 0 .9 times 0 .8 times 0 .7.
00:49
And that comes out to be 0 .504.
00:53
Now part b asks you to find what is the conditional probability.
00:58
What's the probability that she fails the second exam given that she doesn't pass them all? and not passing all, we know that that means we would need to find the probability of, i'll call this event a and this event b.
01:21
We'd find the probability of a intersect b or a and b happening and divided by the probability of b.
01:27
Now, the probability that she doesn't pass all three is the complement of this, 1 minus 0 .504, which is 0 .496.
01:41
However, another way i like to see it a little bit better is let's look at the ways that she doesn't pass.
01:48
It could be she just fails, which is, i'll do this in red.
01:52
She just fails...