Answer:
a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}
b) {0,1,2,3}
c)
![P(X=2) = \dfrac{3}{8}](https://tex.z-dn.net/?f=P%28X%3D2%29%20%3D%20%5Cdfrac%7B3%7D%7B8%7D)
d)
![P(\text{3 boys}) = \dfrac{1}{8}](https://tex.z-dn.net/?f=P%28%5Ctext%7B3%20boys%7D%29%20%3D%20%5Cdfrac%7B1%7D%7B8%7D)
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}
![P(X=2) =\dfrac{3}{8}](https://tex.z-dn.net/?f=P%28X%3D2%29%20%3D%5Cdfrac%7B3%7D%7B8%7D)
d) probability that the couple have three boys.
Favorable outcome: {BBB}
![P(BBB) = \dfrac{1}{8}](https://tex.z-dn.net/?f=P%28BBB%29%20%3D%20%5Cdfrac%7B1%7D%7B8%7D)