China’s one child per couple policy has been in effect since 1979. However, in r

Question

China’s one child per couple policy has been in effect since 1979. However, in rural areas where couples particularly want a boy, families may be allowed to have two children if the first one is a girl. Assume that 51.5% of births are boys.

(a) Consider 1000 rural families who will have a second child if the first is a girl.

i. How many of the families have just one child?

ii. Of the families with two children, how many have two girls and how many have one child of each sex?

(b) Using the results from part (a), find:

i. The number of children in these 1000 families.  

ii. The proportion of boys among the children of these families.

This is the Excel sheet that was given to us with the questions:

Child Birth Policy Stop after a boy For 1000 families Number Children Nuber ofNumber Number Fill in: Blue then green then pink. Look at what is already there to decide how in Family Families boys irls 500 250 125 63 500 250 125 63 Probabilities Number of Children in Famil 0.5 0.5 250 250 188 Probabilit Probability of boy Probability of girl 0.500 0.250 0.125 0.063 5 5 10 10 12 13 12 13 15 16 17 18 19 20 15 16 17 18 19 20 938 688 Average number children in family Proportion of boys among children

Explanation / Answer

There are 3 possibilities:

1. You get a boy. P(B) = 0.515.

2. A girl then a boy. P(GB) = (1-0.515)*0.515 = 0.249775

3. Both are girls. P(GG) = (1-0.515)*(1-0.515) = 0.235225.

a)

i. E(one child) = 0.515*1000 = 515 [ANSWER]

ii. E(GG) = 0.235225*1000 = 235.225 [ANSWER]
E(GB) = 0.249775*1000 = 249.775 [ANSWER]

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b)

i.

E(children) = 515*1 + (1000-515)*2 = 1485 [ANSWER]

ii.

There are 515+249.775 = 764.775 boys. Hence,

P(B) = 764.775/1485 = 0.515. [ANSWER]

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