Genetics/ Probability Problems

[Intr3pid]

Hi,

I'm just stuck on a few questions. Can anyone offer me some assistance?

a) In families with four children, what proportion of the families will have at least one boy?

b) In families with two girls and one boy, what fraction of the families will have the boy as the second child?

c) In family with four children, what fraction of the families will have the gender order male-female-female-male?

I know these questions deal with probability and numbers but I don't know where to begin.

Thanks in advance

 

[paralith]

The only real genetics aspect to this question is to understand this: every time a child is born, it's a fifty-fifty chance whether or not you'll get a boy or a girl, depending on which sex chromosome they get from their father. That means the probability of having a boy is equal to the probability of getting a girl, like a coin toss. So you can treat these problems as though they were coin tosses, using standard probability; the number of desired outcomes over the number of total possible outcomes. So for example with the first question, in a family with four kids, just figure out how many different combinations of boys and girls you can have; BBBB, BBBG, etc. Out of all the possible choices, how many have at least one boy? The rest should be pretty easy from there.

 

[Intr3pid]

Ok, I managed to to parts a and b. Can anyone give me a hint on how to do problem c?

thankx

 

[paralith]

it's rather like a and b combined. you have four children, but now all your possible outcomes include not only BBBB, BBBG, etc, but also the different orders each of those can come in.

 

[Intr3pid]

for part C, how do I find all the possible combinations without writing them all out?

 

[paralith]

writing them out in this case isn't too painful, because there's not a huge amount; but I would check out this page:

http://www.chem.qmul.ac.uk/software/download/qmc/ch5.pdf

for an explanation of permutations and combinations, which deal with probability and order. (I was never very good at that stuff, which is why I'm sending you to an outside source. =p)