It is known that 20% of all farms in a state exceed 160 acres and that 60% of all farms in that state are owned by persons over 50 years old. Of all farms in the state exceeding 160 acres, 55% are owned by persons over 50 years old.
a. What is the probability that a randomly chosen farm in this state both exceeds 160 acres and is owned by a person over 50 years old?
b. What is the probability that a farm in this state either is bigger than 160 acres or is owned by a person over 50 years old (or both)?
c. What is the probability that a farm in this state, owned by a person over 50 years old, exceeds 160 acres?
d. Are size of farm and age of owner in this state statistically independent?