EXAMPLE 4.18 Labor Rates
Averaged over the year 2013, the following table contains counts (in thousands) of persons aged 16 and older in the civilian population, classified by gender and employment status:15
| Gender | Employed | Unemployed | Not in labor force | Civilian population |
|---|---|---|---|---|
| Men | 76,353 | 6,314 | 35,889 | 118,556 |
| Women | 67,577 | 5,146 | 54,401 | 127,124 |
| Total | 143,930 | 11,460 | 90,290 | 245,680 |
The BLS defines the total labor force as the sum of the counts on employed and unemployed. In turn, the total labor force count plus the count of those not in the labor force equals the total civilian population. Depending on the base (total labor force or civilian population), different rates can be computed. For example, the number of people unemployed divided by the total labor force defines the unemployment rate, while the total labor force divided by the civilian population defines labor participation rate.
Randomly choose a person aged 16 or older from the civilian population. What is the probability that person is defined as labor participating? Because “choose at random” gives all 245,680,000 such persons the same chance, the probability is just the proportion that are participating. In thousands,
This calculation does not assume anything about the gender of the person. Suppose now we are told that the person chosen is female. The probability that the person participates, given the information that the person is female, is