An experiment consists in drawing, without replacement, a random sample of size two from a group of five children. There are three boys (Jack, Jim, Joe) and two girls (Jill, Jane). The order of selection does not matter when each pair of chilren are listed. (a) Draw up a list of the points in the sample space (i.e. all possible outcomes). (b) By listing the sample points in each case, find how many sample points correspond to each of the following events: A: Jack and Jill are both chosen, B: Jill is chosen, C: At least one girl is chosen, D: Exactly one boy and one girl are chosen. Now assuming all samples are equally likely, give the probabilities of those four events. (c) Write down all valid inclusion relations, such as A B, which may exist between pairs of the above events. (d) Which pairs of the events A, B, C and D are mutually exclusive? Give reasons