So, you have the initial probability of A (thus P(A)) is
P(A) = 0.7
Likewise, you tell us that
P(B) = 0.8
I could have sworn that probabilities of disjoint events want to add to 1. At least, here, the universe of events is the set {A,B}, where A and B are disjoint events.
Once you resolve that dilemma, write the problem in the form of a 2x2 transition matrix. Call it T,
T = [.8 .2;.3 .7];
Now, create a row vector, that describes the current state. You might call it PAB.
Can you multiply the vector of probabilities by the transition matrix? What would that do for you? (Hint: TRY IT!)
