Children ratio

In a certain office, 1/3 of the workers are women. Of the women, 1/2 are married, and of the married women, 1/3 have children. Of the men, 3/4 are married, and of the married men, 2/3 have children. What fraction of the workers have no children?

Final Answer:

r =  11/18

Step-by-step explanation:

$$\begin{gathered} r_1=\frac{1}{3}\cdot \frac{1}{2}\cdot \frac{1}{3}=\frac{1}{18}\doteq 0.0556 \\ {r}_2=\frac{2}{3}\cdot \frac{3}{4}\cdot \frac{2}{3}=\frac{1}{3}\doteq 0.3333 \\ a=r_1+r_2=\frac{1}{18}+\frac{1}{3}=\frac{1}{18}+\frac{6}{18}=\frac{1+6}{18}=\frac{7}{18}\doteq 0.3889 \\ r=1-a=1-\frac{7}{18}=\frac{1\cdot 18}{18}-\frac{7}{18}=\frac{18}{18}-\frac{7}{18}=\frac{18-7}{18}=\frac{11}{18}=0.6111 \end{gathered}$$

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