conditional probability question?

Question

if p(a) = 0.1 , p(b) = 0.1, p(b|a) = 0.8 [and p(a|b) = 0.8] and p(a or b) = 0.12

what is p(a and b)

Answer 1

Do you know if a and b are dependent?

Dependent answer:
p(a∩b) = p(a) * p(b|a) = 0.1 * 0.8 = 0.08

Independent answer:
p(a∩b) = p(a) * p(b) = 0.1 * 0.1 = 0.01

Answer 2

There's no need for an "independent" answer. They aren't. If they were then we'd have p(a|b)=p(a) which isn't the case.

So p(a and b) = p(a)p(b|a) = 0.08.

Answer 3

P(a and b) = p(a or b) - p(a) = 0.02