**Describe the outcome space**

(a)If a Families that have three children each and select one such family at random. Describe the sample space S in terms of their children as 3-tuple, agreeing for example that "gbb" would indicate that the youngest is a girl and two oldest are boys.

(b) A rat is selected at random from a cage, and its Sex is determined.

(c) A state selects a three-digit integer at random for one of its lottery games.

(a) In this scenario, where families have three children each, the sample space S can be described in terms of their children as 3-tuple. Each tuple will represent the gender of the three children in the family. To represent the gender, we can use the letters "G" for girl and "B" for boy. For example, the sample space S can include tuples like "BBB" (indicating that all three children are boys), "BGB" (indicating that the oldest and youngest children are boys and the middle child is a girl), "GGG" (indicating that all three children are girls), and so on. The sample space S will consist of all possible combinations of "B" and "G" in the 3-tuples.

(b) In this scenario, where a rat is selected at random from a cage, and its sex is determined, the sample space S will consist of two outcomes: male (M) and female (F). The sample space S will be {M, F} representing the possible outcomes of selecting a rat and determining its sex.

(c) In this scenario, where a state selects a three-digit integer at random for one of its lottery games, the sample space S will consist of all possible three-digit integers ranging from 000 to 999. The sample space S will include numbers like 001, 002, 003, ..., 997, 998, 999, forming a set of 1000 distinct outcomes. So, the sample space S will be {000, 001, 002, ..., 998, 999} representing all the possible three-digit integers that could be selected.

(a) The sample space, S, for a family that has three children can be described as the set of all possible outcomes when selecting one such family at random. Each outcome in S can be represented as a 3-tuple, where each element of the tuple represents the gender of a child. For example, if "gbb" represents the youngest child being a girl and the two oldest children being boys, then the sample space S would include all possible combinations of "g" (girl) and "b" (boy) for each child, such as ("ggg"), ("ggb"), ("gbg"), ("gbb"), ("bgg"), ("bgb"), ("bbg"), and ("bbb").

(b) The sample space, S, for determining the sex of a rat selected at random from a cage would consist of the two possible outcomes - male (M) or female (F). Therefore, S = {M, F}.

(c) The sample space, S, for a state selecting a three-digit integer at random for one of its lottery games would consist of all possible three-digit numbers from 000 to 999. Therefore, S = {000, 001, 002, ..., 998, 999}.