1. ## Probability of americans licensedrivers test (fun)

I have really tried as you can see on the buttom of the page but dont know how to proceed. Some help would be greatly appreciated.

QUESTION!
In an american carschool 60% of the attendants pass the official test for the driverslicense. Before doing the offical test have to do a prior test at the carschool.(test nr1)
I has shown that among those attendents who passed the official test (test nr2) on the first try 80% of them had passed the carschooltest (nr1).
Among those attendants who don't pass the official test (nr2) on the first try only 10%has passed test nr 1,.

a) Calculate the probability that an attandant both passes the carschools and the official test?
b) Calculate the probability that an attendandt passes the carschooltest?
c) Calculate the probability that an attendandt who have passed the carschooltest passes the official test for drivers licence.
d) Calculate the probability that an attendant who has managed to pass at least one test now have passed the official test.

So far MY work is stuck after I find this through the formulas on the pic I posted above. We need to clarify Events here. I set
Event A: The attendandt passes the official test for the drivers license for the first time.
Event B: The attendendants passes both the tests,
Event C: The attendendants who passes the carschooltest
Event D: The attendtands who doesnt pass the official test.

But here I get stuck! How am I to chose between statistically indepent and so on (check the pic I linked to in the beginning of the post)

2. Originally Posted by gossen
I have really tried as you can see on the buttom of the page but dont know how to proceed. Some help would be greatly appreciated.

QUESTION!
In an american carschool 60% of the attendants pass the official test for the driverslicense. Before doing the offical test have to do a prior test at the carschool.(test nr1)
I has shown that among those attendents who passed the official test (test nr2) on the first try 80% of them had passed the carschooltest (nr1).
Among those attendants who don't pass the official test (nr2) on the first try only 10%has passed test nr 1,.

a) Calculate the probability that an attandant both passes the carschools and the official test?
b) Calculate the probability that an attendandt passes the carschooltest?
c) Calculate the probability that an attendandt who have passed the carschooltest passes the official test for drivers licence.
d) Calculate the probability that an attendant who has managed to pass at least one test now have passed the official test.

So far MY work is stuck after I find this through the formulas on the pic I posted above. We need to clarify Events here. I set
Event A: The attendandt passes the official test for the drivers license for the first time.
Event B: The attendendants passes both the tests,
Event C: The attendendants who passes the carschooltest
Event D: The attendtands who doesnt pass the official test.

But here I get stuck! How am I to chose between statistically indepent and so on (check the pic I linked to in the beginning of the post)
These are problems using conditional probabilities.

Here is a start. For part (a), let event C be passes car school test, event O be passes official test. Then from the definition of conditional probability

P(C and O) = P(C|O)P(O)

and you are given those probabilities on the right.