00:01
One good way to deal with a problem like this is to use an event tree diagram, or just a tree diagram.
00:08
The first branch represents the first attempt at the exam, and we are told in the question that the probability of passing is 0 .4 on the first attempt.
00:19
So it's obviously a difficult exam, and then the probability of failing is 0 .6.
00:27
Then if a second attempt is made, the probability of passing is 0 .65, which means that the probability of failing this one is 0 .35.
00:40
And then for the third attempt, it says the probability of not passing is 0 .15.
00:48
That means that there is an 85 % chance of passing on the third attempt.
00:55
So for the problem, we are asked, what is the probability of passing the examination, whether that be on the first, second, or a third attempt? so that is all of these branches lead to passing the exam.
01:14
And only this branch leads to failing the exam.
01:21
The probability for passing on the first branch is .4.
01:25
The probability for passing on the second branch is the product of these two probabilities.
01:40
This is 0 .39.
01:42
And the probability for reaching the end of this branch is .6 times .35 times .85 times .85...