Question

A couple plans to have 3 children. The gender of each child is equally likely. Design a simulation involving 35 trials that you can use to model the genders of the children. Write your answers as numbers.

Answer 1

Computers eat this sort of stuff up for a snack. If you like I can run the simulation for you. In the meantime, you can set up the simulation yourself. It is like flipping a coin 35 times.

Child 1 Child 2 Child 3
M M M
M M F
M F M
M F F
F M M
F M F
F F M
F F F

No Males 1/8
1 Male 2 females 3/8
2 Males 1 female 3/8
No Females 1/8

Now you need to deal with the 35

Take each of the probabilities and multiply by 35

No males = 1/8 * 35 = 4.375
1 M 2 Fe = 3/8 * 35 = 13.125
2 M 1 Fe = 3/8 * 35 = 13.125
3 M = 1/8 * 35 = 4.375
Total = 35.

Just in case you are interested, I'll post a simulation of a million trials to see how close they come to the theoretical expectations. I do this in comments a bit later.
It should come to about 1/8, 3/8 3/8 and 1/8. We'll see if it does.

The simulation you seek would be coin tossing. Heads and Tails will give exactly the same results.