**Answer:**

a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

b) {0,1,2,3}

c)

d)

**Step-by-step explanation:**

We are** given the following** in the question:

Suppose a couple planned to have three children. Let X be the number of girls the couple has.

**a) possible arrangements of girls and boys**

Sample space:

{GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

**b) sample space for X**

X is the number of girls couple has. Thus, X can take the values 0, 1, 2 and 3 that is 0 girls, 1 girl, 2 girls and three girls from three children.

Sample space: {0,1,2,3}

**c) probability that X=2**

P(X=2)

That is we have to compute the probability that couple has exactly two girls.

Favorable outcome: {GGB, GBG, BGG}

**d) probability that the couple have three boys.**

Favorable outcome: {BBB}