One Child Policy - By Hand Calculations (Questions #1-3 should be answered witho

Question

One Child Policy - By Hand Calculations (Questions #1-3 should be answered without using the assignment spreadsheet.) China's one child per couple policy was in effect since 1979, and is now being relaxed1. Under the policy, in rural areas where couples particularly want a boy, families were allowed to have two children if the first one is a girl Assume that 51.5% of births are boys and that the sexes of successive babies are inde- pendent2. 1. Consider 1000 rural families who will have a second child if the first is a girl (a) How many of the families have just one child? (b) Of the families with two children, how many have two girls and how many have one child of each sex? 2. Using the results from question 1, find (a) The number of children in these 1000 families (b) The proportion of boys among the children of these families 3. Explain why the answer to 2(b) is to be expected.

Explanation / Answer

1)

a) as if first child is boy then family has only one child for whcih probability is 0.515

terefore number of families with one child =1000*0.515 =515

b)here number of familty with two girls = =1000*0.485*0.485 =235.225

numebr of family with 1 boy and 1 girl =1000*0.485*0.515=249.775

2)

a) number of children =515*1+485*2=1485

b) proportion of boys =(515+249.775)/1485=0.515

b)

as events are independent and proportion is in equilibirium state tehrefore it was expected that proportion of boys shold be same as prior populaiton. same can be found through Hardy Weinberg principal

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