To solve this problem, we need to analyze the possible birth orders and their probabilities. Part 1: Number of Birth Orders As previously calculated, there are 8 possible birth orders for a family with three children, assuming each child can be either a boy (B) or a girl (G) 1. Part 2: Probability Distribution Table We need to determine which of the given options correctly represents the probability distribution of the birth orders. Three girls (GGG): There is 1 way to have all three children as girls. Two girls, one boy (GGB, GBG, BGG): There are 3 ways to have two girls and one boy. One girl, two boys (BBG, BGB, GBB): There are 3 ways to have one girl and two boys. Three boys (BBB): There is 1 way to have all three children as boys. The probabilities for each outcome are calculated as follows: Probability of three girls = 1 8 = 0.125 8 1 =0.125 Probability of two girls, one boy = 3 8 = 0.375 8 3 =0.375 Probability of one girl, two boys = 3 8 = 0.375 8 3 =0.375 Probability of three boys = 1 8 = 0.125 8 1 =0.125 The correct probability distribution table is: Option A: Three girls: 1 8 = 0.125 8 1 =0.125 Two girls, one boy: 3 8 = 0.375 8 3 =0.375 One girl, two boys: 3 8 = 0.375 8 3 =0.375 Three boys: 1 8 = 0.125 8 1 =0.125 Total: 1 Therefore, the correct answer is Option A.b. What is the probability of two boys and a girl? enter your response here (Simplify your answer.)