AS stats - probability questions?

Pr(B') = 1 - Pr(B) = 1/2
Pr(A|B') = 4/5 = Pr(A and B')/Pr(B')

so from this you can figure out that Pr(A and B') = (4/5)(1/2) = 2/5.

Now since Pr(A and B') = Pr(A) = 2/5, you know A and B' are independent. Therefore A and B are independent. So Pr(A and B) = Pr(A)*Pr(B) = (2/5)*(1/2) = 1/5.

Pr(A or B) = Pr(A) + Pr(B) - Pr(A and B) = (2/5) + (1/2) - (1/5) = 7/10.
Pr(A|B) = Pr(A) = 2/5 since A and B are independent, or you could double check with:
Pr(A|B) = Pr(A and B)/Pr(B) = (1/5) / (1/2) = 2/5