Question

A couple wants to have three children. Assume that the probabilities of a newborn being male or female are the same and that the gender of one child does not influence the gender of another child.

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The future parents are wondering how many boys they might get if they have three children. Give a probability model (sample space and probabilities of outcomes) for the number of boys.


What is the sample space?

Answer 1

The sample space represents all the possible outcomes of a random experiment. In this case, the random experiment is the gender of three children. Since each child can be either a boy or a girl, the sample space for the number of boys can be represented as follows:

Sample Space = {BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG}

In this sample space, B represents a boy and G represents a girl. Each outcome in the sample space represents a combination of genders for the three children. For example, BBB means all three children are boys, BBG means two boys and one girl, and so on.

The sample space consists of all possible combinations of boys (B) and girls (G) among the three children.

Answer 2

The sample space in this scenario represents all the possible outcomes of having three children. Each outcome consists of a combination of three genders (either male or female) for the three children.

The sample space can be represented as follows:

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

Each element in the sample space represents a possible outcome. For example, BBB represents all three children being boys, BBG represents the first two children being boys and the third child being a girl, and so on.

There are a total of 8 possible outcomes in the sample space, reflecting all the different combinations of genders for three children.