I have the following problem:
Given that P(A) = 0.7, P(B) = 0.5 and P(A|B) = 0.8, find
a. P(A∩B)
b. P(A∪B)
C. P($B^c$|A)
Here is my approach:
a. P(A∩B) = P(A|B)$*$P(B) = 0.8$*$0.5 = 0.4
b. P(A∪B) = P(A) + P(B) - P(A∩B) = 0.7 + 0.5 - 0.4 = 0.8
c. P($B^c$|A) = 1 - P(B|A) = 1 - $\frac{P(B∩A)}{P(A)}$ = 1 - $\frac{P(A∩B)}{P(A)}$ = 1 - $\frac{0.4}{0.7}$ = $\frac{3}{7}$ = 0.429
With problems like these, how can I decide whether the two events are dependent or not? And if they were, did I follow the right steps to solve these problems?
I can't help but feel like I messed up somewhere, and I would really appreciate some correction. I thank you for any and all contribution!