A mother and her children

A MOTHER AND HER CHILDREN  

1) You meet a mother who tells you 

“I have two children.”

What is the probability that her other child is a boy? 

2) Now suppose she tells you

‘I have 2 children and the oldest is a boy.”

What is the probability that the other one is a boy?

3) Make up a similar problem to this for a family of three children and show your answers.

The Answer:  The two possible answers share a number of assumptions. First, it is assumed that the space of all possible events can be easily enumerated, providing an extensional definition of outcomes: {BB, BG, GB, GG}.[10] This notation indicates that there are four possible combinations of children, labelling boys B and girls G, and using the first letter to represent the older child. Second, it is assumed that these outcomes are equally probable.[10] This implies the following model, a Bernoulli process with p = 1/2

Each child is either male or female.

Each child has the same chance of being male as of being female.

The sex of each child is independent of the sex of the other.

The mathematical outcome would be the same if it were phrased in terms of a coin toss.