You are Here: Home >< Maths

# Tree diagram help watch

1. Hello

I've just seen this question in a past paper and im stuck on it. I don't really know how i should start the tree diagram. Do i have to start with male and female? All the possibilites like 4girls 4 boys, 3 girls 1 boy, 3 boys 1 girl, 2 boys 2 girls?
I am stuck. Wouldnt the probabilites always be 1/2 as it as half as likely to get a boy or girl?

Here is the question:

Assume that couples will never have more than 4 childrean (in total). Draw a tree diagram representing all the possibilities. Use this tree diagram (and associated probabilities) to work out the expected number of children in a family.

Thanks
2. firstly im assuming you mean 4 boys 0 girls.

Each node of the tree would have male and female branches.

/ \
male female
/ \ / \
male female male female

etc. etc.

As for the probabilities, to simplify down to 2 children.

male male = 1/2 * 1/2
male female = 1/2 * 1/2
female male = 1/2 * 1/2
female female = 1/2 * 1/2

so each of the above are 1/4. however there are 2 outcomes where you have one male and one female so you add them. so one male one female = 1/4+1/4 = 1/2.

Is that clear? Sorry not ideal using only text.
3. Won't you have to include the possibilities that they could have 0/1/2/3 children? Sorry if I've misunderstood entirely, but it says NO MORE than 4 children, so they could have all the possible combinations of Boy, Girl etc, plus the possibilities of having less than 4...not that I know what those possibilities would be
4. Ok i think i may have totally missed the point of the question

How many marks is the question? / Which paper is it from?
Is there any other data attached to the question?
5. Its from an old uni paper.

The first question of it I had to work out the average size of a family. There were 250 numbers in groups of 5 with numbers 0-9 where I had to use 20 simulations.

I used 0-4 for boys and 5-9 for girls. It worked out as the average size of family as 5.

Im still not really sure what to do, with how many branches to use or what to call them...

Thanks
6. (Original post by LoveBites)
Won't you have to include the possibilities that they could have 0/1/2/3 children?
Yes, you're exactly right. And I don't know how to do it either, and I'm a third year maths undergraduate. Interesting.

Perhaps you're meant to treat each sequence, e.g. "girl, then boy, then no more kids", as having equal probability to any other sequence. But that seems stupid. And of course you can't just say the probability of a boy is 1/2 and the probability of a girl is 1/2, because there's always the probability that they'll have no kids...

I can't think of anything sensible to do.
7. Then wouldn't there be three lines at the beginning each with a 1/3 probability? Male, female, none? Then carry on like that from each stem that would result in a child? Like this (B-boy, g-girl, n-none)

*sorry, the unnamed third stem after GIRL is none (no children), forgot to name it in paint
8. (Original post by mcp2)
Then wouldn't there be three lines at the beginning each with a 1/3 probability?
Why would they all have the same probability?
9. Unless told otherwise wouldn't you expect it that way? Say we were told that every family had at least 1 child, then the probability would be 1/2, but here the questions allows the family to have at the very least, 1 girl, 1 boy or no child.

And I think I made a mistake on the tree diagram, if they didn't have a child after the 1st, or 2nd then it would just stop right? It wouldn't have to go onto a branch with "no child", or would it?
10. I see no way of answering the question given the information provided. I think the OP needs to post the entire question (including earlier parts).
11. Here are the first two questions:

2. many couples want to have both a boy and a girl. If they decide to continue to have children until they have one child of each sex, we would like to know what would be the average size of each family, assuming boys and girls are equally likely.

a) Clearly describe how you would use the table of random numbers below to undertake a simulation to find this out. Then make your own estimate of the average size, using at least 20 simulations, carefully saying what you are doing. (Start with the first random digit.(

36460 53772 66635 25045 79007 78518 73580 14191 50353 32064 13205 69237 21820 20952 16635 58867 97650 82983 64865 93298 51242 12215 90739 36812 00436 31609 80333 96606 30430 31803 67819 00354 91439 91073 49258 15992 41277 75111 67496 68430 09875 08990 27656 15871 23637 00952 97818 64234 50199 05715

The first question of it I had to work out the average size of a family. There were 250 numbers in groups of 5 with numbers 0-9 where I had to use 20 simulations.

I used 0-4 for boys and 5-9 for girls. It worked out as the average size of family as 5.

b) Now in addition, assume that couples will never have more than 4 childrean (in total). Draw a tree diagram representing all the possibilities. Use this tree diagram (and associated probabilities) to work out the expected number of children in a family.

Thanks
12. Firstly, let me observe that it was indeed completely impossible to answer this question from the information in your original post. Please read the Guide to Posting, which tells you to "post your question clearly, with no inaccuracies, and nothing relevant missed out".

Anyhow, now we have the full question:

Your tree will start off by considering the sex of the first birth. That is, you will have two branches, one for '1st = girl', one for '1st = boy'.
Then for each branch, you have two subbranches for the two possible sexes of the 2nd birth.
At this point, some parts of the tree will terminate. For example, if the 1st birth is a girl, and the 2nd a boy, then there will be no subsequent births.
Otherwise, you need to consider the 3rd birth, and then possibly the 4th.

Edit: I've also just done a (computer) simulation using the random numbers you gave. I don't see how you get 5 as an average - my answer is much smaller.
13. Bonus question: suppose there's no limit on the size of a family. What's the expected number of children?
14. I averaged 3 children, then the mother and father
15. So it would look sort of like this:

How would I work out the probability because its the same probability that it will be a boy and girl?

Thanks
16. So p(G) = p(B) = 0.5.
17. Thanks. Does the tree diagram look morealess what its meant to?
18. Yes.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: July 20, 2009
The home of Results and Clearing

### 2,057

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams