Respuesta :
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
[tex]P = (0.5)^{3} = 0.125[/tex]
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
[tex]P = (0.5)^{4} = 0.0625[/tex]
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
[tex]P = (0.5)^{5} = 0.03125[/tex]
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
[tex]P = (0.5)^{6} = 0.015625[/tex]
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
