A group of 8 children go on a field trip. Mrs. Smith is the mother of 3 of these children. School officials later announce that 2 of the children in the group were exposed to hepatitis while on the trip, but they provide no information as to which 2 children were exposed.

(a) What is the probability that both of the exposed children were Smith children?

(b) What is the probability that exactly one of the two exposed children was a Smith?

(c) What is the probability that at least one of the two exposed children was a Smith?

(d) What is the probability that neither exposed child was a Smith?

(e) One of Mrs. Smith's children in the group is named Amy. What is the probability that Amy Smith was one of the two exposed children?

(f) School officials contact Mrs. Smith to let her know that Amy was one of the two exposed children. What then is the conditional probability that the other exposed child is one of her other children?