If A = { Market research predicates strong demand } and B = { Market demand is strong }, can we reasonably assume that P(A or B) = P(A) * P(B)?
The problem is that I know
- P(B|A) = 0.8
- P(not B | not A) = 0.9,
- P(B) = 0.2
I need to calculate P(A) and P(not A).
For me, it seems that if P(A or B) != P(A) * P(B), it's impossible to know the answer.
Actually, I'm drawing a decision tree to determine whether a market research is worth trying. All the information is listed above. Without P(A) and P(not A), I can not determine calculate the expected value of the branch of taking the research and can not draw the tree.