A group consists of equal number of men and women. Of this group 20% of the men and50% of the women are unemployed. If a person is selected at random from this group, find theprobability of the selected person being employed.
Question
A group consists of equal number of men and women. Of this group 20% of the men and50% of the women are unemployed. If a person is selected at random from this group, find theprobability of the selected person being employed.
Solution
Sure, let's break this down:
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We know that the group consists of an equal number of men and women. Let's assume that there are 100 men and 100 women to make the calculations easier.
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20% of the men are unemployed. This means that 20 men are unemployed, leaving 80 men who are employed.
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50% of the women are unemployed. This means that 50 women are unemployed, leaving 50 women who are employed.
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The total number of people in the group is 200 (100 men + 100 women).
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The total number of employed people in the group is 130 (80 employed men + 50 employed women).
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The probability of selecting an employed person at random from the group is the number of employed people divided by the total number of people.
So, the probability is 130/200 = 0.65 or 65%.
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