Discussion
In a year there are 900 births in a town a of which 51.5% were males, while in town a and b combined, this proportion in a total of 1350 births was 0.50. What is the proportion of male births in the town b ?
Answer: A
The proportion of male births in town b is 0.47.
Count the males and births in each town:
\[ \begin{aligned} \text{Males in a} &= 0.515 \times 900 = 463.5 \\ \text{Males in a and b} &= 0.50 \times 1350 = 675 \\ \text{Births in b} &= 1350 - 900 = 450 \\ \text{Males in b} &= 675 - 463.5 = 211.5 \end{aligned} \]
\[ \frac{211.5}{450} = 0.47 \]
Since town a is above the combined proportion of 0.50, town b must lie below it, which rules out 0.50 and 0.51. 0.49 is what a simple guess between the two would give, but the towns have unequal numbers of births, so the proportions must be weighted.
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