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Consider the following contingency table of 50 people classified according to gender and employment status. If one person is selected randomly.

Employment Status
Gender Full-part Part-time Unemployed
Male 20 7 3
Female 10 4 6
Calculate the probability that the person is either male or a full-time employee.

1 Answer

5 votes

Out of the 50 people in the contingency table, the number of males is 20+7+3 = 30 and the number of full-time employees is 20. However, we cannot simply add these numbers together to get the number of people who are either male or full-time employees because there are some people who are both male and full-time employees, and we don't want to count them twice.

To correct for this, we need to subtract the number of people who are both male and full-time employees (which is 20) from the total number of people who are male or full-time employees (which is 30+20 = 50). Therefore, the number of people who are either male or full-time employees (or both) is 50-20 = 30.

The probability that the person is either male or a full-time employee is therefore:

P(male or full-time employee) = number of people who are either male or full-time employees / total number of people

P(male or full-time employee) = 30/50

P(male or full-time employee) = 0.6

Therefore, the probability that the person is either male or a full-time employee is 0.6, or 60%.

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