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Select the correct answerIn 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?Options11/18 4/95/1817/36

Question

Select the correct answerIn 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?Options11/18 4/95/1817/36

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Solution

To solve this problem, we need to break it down into several steps:

  1. First, let's find out the proportion of women who are married and have children. We know that 1/2 of the women are married and 1/3 of these married women have children. So, the proportion of women who are married and have children is 1/2 * 1/3 = 1/6.

  2. Similarly, we can find out the proportion of men who are married and have children. We know that 3/4 of the men are married and 2/3 of these married men have children. So, the proportion of men who are married and have children is 3/4 * 2/3 = 1/2.

  3. Now, let's find out the proportion of women and men in the office who have children. We know that 1/3 of the workers are women, so the proportion of workers who are women and have children is 1/3 * 1/6 = 1/18. Similarly, we know that 2/3 of the workers are men (since 1 - 1/3 = 2/3), so the proportion of workers who are men and have children is 2/3 * 1/2 = 1/3.

  4. Adding these two proportions together, we find that the proportion of workers who have children is 1/18 + 1/3 = 7/18.

  5. Finally, to find the proportion of workers who do not have children, we subtract the proportion of workers who have children from 1 (since the total proportion of workers is 1). So, the proportion of workers who do not have children is 1 - 7/18 = 11/18.

So, the correct answer is 11/18.

This problem has been solved

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