Joint and conditional probabilities. P(A) = 0.3, P(B) = 0.7
(a) Can you compute P(A and B) if you only know P(A) and P(B)?
(b) Assuming that events A and B arise from independent random processes,
i. what is P(A and B)?
ii. what is P(A or B)?
iii. what is P(A|B)?
(c) If we are given that P(A and B) = 0.1, are the random variables giving rise to events A and B independent?
(d) If we are given that P(A and B) = 0.1, what is P(A|B)?