Probability question I'm having difficulty with

• July 11th 2013, 08:34 PM
Smb122
Probability question I'm having difficulty with
To gauge the relationship between education and unemployment an economist turned to the US Census, from which the following table was produced:

(First number represents employed, second number represents unemployed)
Not a high school graduate 0.0975 , 0.0080
High school graduate 0.3108 , 0.0128
Some college, no degree 0.1785 , 0.0062
Associate’s degree 0.0849 , 0.0023
Bachelor’s degree 0.1959 , 0.0041

a. What is the probability that a high school graduate is unemployed?
b. Determine the probability that a randomly selected individual is employed.
c. Find the probability that an unemployed person possesses an advanced degree.
d. What is the probability that a randomly selected person did not finish high school?
Data from the Office on Smoking and Health, Centers for Disease Control and Prevention, indicate that 40% of adults who did not finish high school, 34% of high school graduates, 24% of adults who completed some college (no degree), and 14% of graduates (Degree holders) smoke.
e. Suppose that one individual is selected at random and it is discovered that the individual smokes. What is the probability that the individual is a graduate? (Use the probabilities from the table above to solve this question)

HINT:
Conditional probability: P(A|B) = P(A and B)/P(B)

Bayes’ Law Formula:
P(Ai |B)= ]P(Ai)P(B|Ai)] / [P(A1 )P(B | A1 ) + P(A 2 )P(B | A 2 ) + . . . + P(A k )P( B | A k )]
• July 12th 2013, 07:25 AM
HallsofIvy
Re: Probability question I'm having difficulty with
Have you tried anything at all?

Personally, I would not use "Bayes formula" or the "Conditional probability" formula.

Instead I would calculate specific numbers. Suppose our pool consists of 1000000 people. Then
"Not a high school graduate 0.0975 , 0.0080"
So we have 0.0975*1000000= 97500 non-high school graduates who are employed, 0.0080*1000000=8000 who are unemployed.

"High school graduate 0.3108 , 0.0128"
So we have 0.3108*1000000= 310800 high school graduates who are employed, 0.0128*1000000= 12800 high school graduates who are unemployed.

"Some college, no degree 0.1785 , 0.0062"
So we have .01785*1000000= 178500 people with some college who are employed, 0.0062*1000000= 6200 people with some college who are unemployed.

"Associate’s degree 0.0849 , 0.0023"
So we have 0.0849*1000000= 84900 people with associate's degree who are employed, 0.0023*1000000= 2300 people with associate's degree who are unemployed.

"Bachelor’s degree 0.1959 , 0.0041"
So we have 0.1959*1000000= 195900 people with bachelor's degree who are employed, 0.0041*1000000= 4100 people with bachelor's degree who are unemployed.

Fourth was "The probability that a randomly selected person did not finish high school". There were 97500 non high school graduates who were employed, 8000 who were not so a total of 97500+ 8000= 105500 non high school graduates out of 1000000. The probability of any one of those 1000000 people being a non high school graduate is $\frac{105500}{1000000}$.