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In a monogamous culture, 90% of the adults are married. The

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In a monogamous culture, 90% of the adults are married. The [#permalink] New post 07 Sep 2004, 10:03
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In a monogamous culture, 90% of the adults are married. The average number of children per family is five and over-population is a threat. Programs to encourage birth-control have been ineffective. It has been suggested that this failure is due to these programs ignoring a tradition that values male children very highly, so that every parent wants to have at least one son. It is proposed that couples be encouraged to use birth-control measures after the birth of their first son. If this proposal is widely accepted in the culture, we may expect that:

(A) the rate of population increase will be slowed, and future generations will contain a disproportionately high number of females.

(B) the rate of population increase will be slowed, and the gender balance in future generations will remain as it is at present.

(C) the rate of population growth will remain the same, and future generations will contain a disproportionately high number of females.

(D) there will be no significant effect either on population growth or on gender balance.

(E) the population will decline precipitously, because approximately half of all families will have only a single child.

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 [#permalink] New post 07 Sep 2004, 10:18
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 [#permalink] New post 07 Sep 2004, 10:27
Assuming this culture has no "natural" reproductive tendency to give birth to female children, E appears to be the best asnwer. That is, the answer assumes that you have an equal chance of bearing a male or a famle child the first/next time.

As it is, it looks as if families like to have to one, two, three...read: several...male children. Asking them to stop at the first will degenerate this spawning.

On a long-term basis, if there's a 50% chance of bearing a male child, there's a good likelihood that you'll have one male child out of every two. The average will, then, be:

Pr(first child = male) * 1 male child + Pr(first child = female) * Pr(second child = male) * 2 children + Pr(first child = female) * Pr(second child = female) * Pr(second child = female) * 3 children + ...

= (0.5)(1) + (0.5)(0.5)(2) + (0.5)(0.5)(0.5)(3) + (0.5)(0.5)(0.5)(0.5)(4) + (0.5)(0.5)(0.5)(0.5)(0.5)(5) ...

= 0.5 + 0.5 + 0.375 + 0.25 + 0.15625 + ...

= sum from 1 to infinity of [n * (0.5)^n] = 2

Thus, the long-term average will fall to 2 children per family.
  [#permalink] 07 Sep 2004, 10:27
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