Probability

[sportywarbz]

The personnel department of Franklin National Life Insurance compiled the data below regarding the income and education of its employees.

Income $50,000 or Below Income Above $50,000
Noncollege Graduate 1980 860
College Graduate 410 750


Let A be the event that a randomly chosen employee has a college degree and B the event that the chosen employee's income is more than $50,000.
Find each of the following probabilities: (Round your answers to four decimal places.)
P(A) = .29
P(A intersection B) =
P(B | A) =
P(B | A^c) =

I don't know what equation to use to solve P(A intersection B). Thanks.

 

[galactus]

\(\displaystyle \begin{array}{c|c|c|c}\text{Income}&\leq 50000&>50000&\text{total}\\ \hline \text{non-college grad}&1980&860&2840\\ \hline\text{college grad}&410&750&1160\\ \hline\text{total}&2390&1610&4000\end{array}\)

\(\displaystyle P(A\cap B)\) is given in the chart. It's at the intersection of college grads and over 50,000. Divide that by the overall total.

\(\displaystyle P(B|A)=\text{probability income is over 50,000 given they're a college grad}\)

Go down the >50000 column to the college grad row. Divide the number at the intersection by the total at the college grad row.

\(\displaystyle \frac{750}{1160}=\frac{75}{116}\approx .647\)

Now, try \(\displaystyle P(B|A^{c})=\text{earn over 50000 given they are not a college grad}\)

\(\displaystyle A^{c}\) is A complement. Those not having a college degree.

 

[sportywarbz]

Thank you! This makes a lot more sense. Our table didn't look like that, which I think threw me off. You're table really helped! Thank you!