Question

Suppose a couple decided to keep having children until they have a girl. Which of these is most likely?A)The couple having 5 children B)The couple having 3 children C)The couple having 4 children D)The couple having 6 children

Answer 1

Answer:

B) The couple having 3 children

Step-by-step explanation:

For each children, there is a 50% probability that it is a girl and a 50% probability that it is a boy.

Suppose a couple decided to keep having children until they have a girl.

The probability that they have 3 children, that is 2 boys before a girl is:

The desired outcome is two boys then a girl. Each of these outcomes has a 50% probability. So

$P = (0.5)^{3} = 0.125$

The probability that they have 4 children, that is 3 boys before a girl is:

The desired outcome is three boys then a girl. Each of these outcomes has a 50% probability. So

$P = (0.5)^{4} = 0.0625$

The probability that they have 5 children, that is 4 boys before a girl is:

The desired outcome is four boys then a girl. Each of these outcomes has a 50% probability. So

$P = (0.5)^{5} = 0.03125$

The probability that they have 6 children, that is 5 boys before a girl is:

The desired outcome is five boys then a girl. Each of these outcomes has a 50% probability. So

$P = (0.5)^{6} = 0.015625$

Which of these is most likely?

The largest probability is the one of them having three children, that is, two boys before a girl.

So the correct answer is:

B) The couple having 3 children