Conditional Probability - Problem 2
The example we're going to look at now is involving testing in my class. So I gave two tests 90% of the class passed the first and 80% passed both; find the probability that a student passed the second given they also passed the first.
So this is actually a problem involving conditional probability because we are given a information of something that already happened given that they passed the first, so that has to happen no matter what. So what we have is conditional probability and so we're going to go to our equation, the probability of a sorry we'll do the order that6 you're probably used to, probability of b given a is equal to the probability of say A and B over the probability of A.
And in this case this is B given A, the given is that they pass the first test, so in our case the A is going to be the first and the B is going to be the second.
So probability that they passed the second given the first is the probability that they pass the first and the second which we can go to our problem and see that 80% passed both and 80% is actually a probability remember that probability is always a number between 0 and 1, 80% is a decimal as .8 so this is actually a probability let me just put this into our equation, this is equal to .8 over the probability of A and A is a probability that they passed the first test which is 90%, so what we end up with is .8 over .9 which is just going to be 8/9 or around 88%.
So using our equation of conditional probability to find the conditional event that a student pass the second given they pass the first.