Beginner level Conditional Probability ( Two students Amy and Betty are taking the same course this term.) Attend Class Tomorrow

[newbie99]

I just start learning conditional probability this term, not sure how to calculate this question.

Two students Amy and Betty are taking the same course this term.
Suppose (i) Amy attends class 50% of the time, (ii) Betty attends class 70% of the time, and
(iii) given that Amy attends the class, the chance for Betty to attend the class is 90%.
Let A = {Amy attends the class tomorrow}, and B = {Betty attends the class tomorrow}.

I believe the event A and B are not independent, because P(A∩B) does not equal to P(A) x P(B). The are not exhaustive neither because P(A) + P(B) does not equal to 1(correct me if i am wrong)

a) Given that at least one of the two students attend the class tomorrow, what is the probability that Amy attends the class tomorrow?
b) Given that at most one of the two students attend the class tomorrow, what is the probability that Amy attends the class tomorrow?

thank you

 

[BigBeachBanana]

Let's start with a)

Can you list the possible outcomes that at least one of the two students attend the class tomorrow?

 

[pka]

Can you find [imath]\mathcal{P}(A\cap B)=?[/imath]

[imath][/imath][imath][/imath]