If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he/she is in the force labor? Show your work.
Given for college graduates:
total pop = 51,582
in labor force = 40,390
employed = 39, 293
I tried using the Case 1 equation but I am sure that I used the numbers incorrectly because I kept on getting big numbers like 400 or something. Please help?
Thanks!
The probability of being in the labor force for anyone would be 40,390/51,582. If you want to include age and education factors, multiply those probabilities by the one you obtained above.
What is the difference in definition between being in the "labor force" and being "employed"?
I hope this helps. Thanks for asking.
To calculate the probability that a randomly chosen college graduate aged 25 years or older is in the labor force, you need to use conditional probability. The formula for conditional probability is:
P(A|B) = P(A ∩ B) / P(B)
In this case:
A = Being in the labor force
B = Being a college graduate aged 25 years or older
First, we need to find the probability of being a college graduate aged 25 years or older:
P(B) = Number of college graduates aged 25 or older / Total population
P(B) = 51,582 / Total population
Next, we need to find the probability of being both a college graduate aged 25 years or older and in the labor force:
P(A ∩ B) = Number of college graduates aged 25 or older in the labor force / Total population
P(A ∩ B) = 40,390 / Total population
Finally, we can substitute these values into the conditional probability formula to calculate the probability of being in the labor force given that the person is a college graduate aged 25 or older:
P(A|B) = (40,390 / Total population) / (51,582 / Total population)
After simplifying the formula:
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = 40,390 / 51,582
Now you can compute the actual value using the given numbers.
P(A|B) = 0.7839
So, the probability that a randomly chosen person who is 25 years of age or older and is a college graduate is in the labor force is approximately 0.7839 or 78.39%.