# Can someone help me on this probability problem

#### Schuyla

##### New member
[FONT=&quot]10. [/FONT][FONT=&quot]In an attempt to reduce the growth of its population, China instituted a policy limiting a family to one child. Rural Chinese suggested revising the policy to limit families to one son. Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl, explain how to use simulation to answer the following:[/FONT]
[FONT=&quot]What would be the average family size?
[/FONT][FONT=&quot]What would be the ratio of newborn boys to newborn girls?

I need some help understanding how to do this problem.[/FONT]

#### Schuyla

##### New member
Thank you for your assistance. I was able to figure it out early this morning.

#### IheartMath

##### New member
10. In an attempt to reduce the growth rate of its population, China instituted a policy limiting a family to one child. After learning of the new policy from the trade show exhibiting used to promote the new policy, Rural Chinese responded and suggested revising the policy to limit families to one son. Assuming the suggested revised policy is adopted and that any birth is as likely to produce a boy as a girl, explain how to use simulation to answer the following:
What would be the average family size?
What would be the ratio of newborn boys to newborn girls?

I need some help understanding how to do this problem.
Can you post the answer you ended up with here? It looks alike a lot of important information is missing, but the main question I have is about the rural policy suggested revision. Does this mean you can only have one son, but as many daughters as you want, or all the girls you want up until you have a boy?
Also, what is the ratio of population between city and rural, or does the revised policy apply to both populations?
I think its more complicated than it seems...

Last edited:

#### soroban

##### Elite Member
Hello, Schuyla!

10. In an attempt to reduce the growth of its population,
China instituted a policy limiting a family to one child.
Rural Chinese suggested revising the policy to limit families to one son.
Assuming the suggested policy is adopted and that any birth is as likely to produce a boy as a girl,
explain how to use simulation to answer the following:

(a) What would be the average family size?

(b) What would be the ratio of newborn boys to newborn girls?
. . I don't understand what they want here.

I don't understand the designation "Rural Chinese".
I will assume that the revised policy applies to all Chinese families.
I assume further than a family may have as many girls as they want,
. . but must stop when a boy is born.

Let F = father, M = mother, G = girl, B = boy.

Then we have these facts:

Code:
      Family   Size   Prob.
------   ----   -----
FMB        3     1/2
FMGB       4     1/4
FMGGB      5     1/8
FMGGGB     6     1/16
FMGGGGB    7     1/32

and so on.
Hence, we have: . . . .E . = . 3(1/2) + 4(1/4) + 5(1/8) + 6(1/16) + 7(1/32) + . . .

Multiply by 1/2: .(1/2)E . = . . . . . . . .3(1/4) + 4(1/8) + 5(1/16) + 6(1/32) + . . .

Subtract: . . . . . .(1/2)E . = . 3(1/2) + (1/4) .+ (1/8) .+ (1/16) .+ (1/32) + . . .

We have: . (1/2)E . = . 1 + (1/2) + (1/4) + (1/8) + (1/16) + (1/32) + . . .
. . . . . . . . . . . . . . . . . \________________________________________/
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
geometric series

The geometric series has a sum of 2.

Therefore: .(1/2)E .= .2 . . $$\displaystyle \rightarrow$$ . . E .= .4

The average family size is 4 people.