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In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4  of the men are married and 2/3  of the married men have children, what part of the workers are without children?

Question

In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4  of the men are married and 2/3  of the married men have children, what part of the workers are without children?

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Solution

Let's break this down:

  1. 1/3 of the workers are women, which means 2/3 of the workers are men.
  2. 1/2 of the women are married and 1/3 of these married women have children. This means 1/2 * 1/3 = 1/6 of the women have children.
  3. Since 1/3 of the workers are women, this means 1/3 * 1/6 = 1/18 of the workers are women with children.
  4. 3/4 of the men are married and 2/3 of these married men have children. This means 3/4 * 2/3 = 1/2 of the men have children.
  5. Since 2/3 of the workers are men, this means 2/3 * 1/2 = 1/3 of the workers are men with children.
  6. Adding the fractions of workers who are women with children and men with children, we get 1/18 + 1/3 = 7/18 of the workers have children.
  7. To find the fraction of workers without children, we subtract the fraction of workers with children from 1 (since all workers are either with children or without children). This gives us 1 - 7/18 = 11/18.

So, 11/18 of the workers are without children.

This problem has been solved

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