Show that if one event a is contained in another event b (i. e., a is a subset of b), then p(a) ≤ p(b). [hint: for such a and b, a and b ∩ a' are disjoint and b = a ∪ (b ∩ a'), as can be seen from a venn diagram.] since a is contained in b, we may write b as , the union of two mutually exclusive events. then p(b) = and p(b) = . then, since it follows that p(b) ≥ . this proves the statement. for general a and b, what does this imply about the relationship among p(a ∩ b), p(a) and p(a ∪ b)? p(a) ≤ p(a ∩ b) ≤ p(a ∪ b) p(a ∪ b) ≤ p(a ∩ b) ≤ p(a) p(a) ≤ p(a ∪ b) ≤ p(a ∩ b) p(a ∩ b) ≤ p(a) ≤ p(a ∪ b) p(a ∩ b) ≤ p(a ∪ b) ≤ p(a)