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?Options5/1811/1817/36 4/9
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?Options5/1811/1817/36 4/9
Solution
To solve this problem, we need to break it down into several steps:
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First, let's find out the proportion of workers who are women and have children. We know that 1/3 of the workers are women, 1/2 of these women are married, and 1/3 of these married women have children. So, the proportion of workers who are women and have children is 1/3 * 1/2 * 1/3 = 1/18.
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Next, let's find out the proportion of workers who are men and have children. We know that 2/3 of the workers are men (since 1/3 are women), 3/4 of these men are married, and 2/3 of these married men have children. So, the proportion of workers who are men and have children is 2/3 * 3/4 * 2/3 = 1/3.
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To find out the proportion of workers who have children, we add the proportion of women who have children to the proportion of men who have children. So, 1/18 + 1/3 = 1/18 + 6/18 = 7/18.
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Finally, to find out the proportion of workers who do not have children, we subtract the proportion of workers who have children from 1 (since all workers either have children or do not have children). So, 1 - 7/18 = 11/18.
Therefore, the proportion of workers who do not have children is 11/18.
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