Mutiplication Rule, Conditional Probability

[melomel]

The probability is 0.6 that a student will study for a History test. If the student studies, she has a 0.8 probability of getting an A. If she doesn't study, she has a 0.3 probability of getting an A. What is the probability that the student gets an A?

So far I made a tree diagram for this experiment but I need help on deciding what to plug into the formula

 

[Unknown008]

Well, if you can think of it, it's not difficult, nor you need the formula.

P(She gets an A) = P(She studies and gets A) or P(She doesn't study and still gets an A)

Which means you have to add both.

P(She gets an A) = P(She studies and gets A) + P(She doesn't study and still gets an A)

P(She studies and gets A) = P(She studies) x P(She gets A while studying)

P(She doesn't study and still gets an A) = P(She doesn't study) x P(She gets A while not studying)

Can you figure out those 4 probabilities? With those, you simply multiply and add to get the final answer.

Can you post your answer? =)