Answer:
After a couple of months of searching for a job, Sofia is hired. Neither the labor force nor the labor force participation rate increase.
Explanation:
The labor force is defined as the sum of all people employed people plus unemployed people who are looking for a job. Sofia was unemployed, but she was searching for a job, so according to the definition, she was and still is a part of the labor force.
Then, the labor force participation rate is defined as the rate of the labor force (defined above) divided by the working-age civilian population. Since Sofia never stopped being a part of the labor force since she had been looking for a job, the change of her employment status doesn't reflect any changes in the labor force participation rate.
