Question

The Pew Research Center finds that the demographic make-up of political parties is changing drastically through the election cycles. Consider the following summary of education levels among party lines

Democrat Republican Total
College Degree 37 31 68
No College Degree 63 69 132
Total 100 100 200
(a) What is the probability a randomly selected participant has a college degree?
(b) What is the probability that a randomly selected participant is a democrat?
(c) What is the probability that a randomly selected participant is a democrat and has a college degree?
(d) Of those who have college degrees, what is the probability of being a democrat?
(e) What is the probability of begin a democrat or having a college degree?
(f) Are having a college degree and being a democrat disjoint events?
(g) Are having a college degree and being a democrat independent events?

Answer 1

(a)0.34

(b)0.5

(c)0.185

(d)0.544

(e)0.655

(f)Not disjoint events

(g)Independent events

Explanation:

The summary of education levels among party lines is given in the table below

`\left|\begin{array}ccc&$Democrat &$Republican &$Total\\--&--&--&--\\$College Degree &37 &31 &68\\$No College Degree& 63 &69 &132\\--&--&--&--\\$Total &100 &100& 200\end{array}\right|`

(a)Probability a randomly selected participant has a college degree.

The probability a randomly selected participant has a college degree is:

`=(68)/(200) =0.34`

(b)The probability that a randomly selected participant is a democrat.

`=(100)/(200) =0.5`

(c)The probability that a randomly selected participant is a democrat and has a college degree.

`=(37)/(200) =0.185`

(d)Probability of being a democrat given that the participant has a college degree.

`=(37)/(68) \approx 0.544`

(e)The probability of begin a democrat or having a college degree

Number of Democrats =100

Number of Those with College degrees = 68

Number of democrats with College degrees =37

Therefore:

Probability of begin a democrat or having a college degree

`=(100+68-37)/(200) \\=(131)/(200)\\\\=0.655`

(f)The event of having a college degree and being a democrat are not disjoint events as there are some democrats who have a college degree.

(g)The event of having a college degree and being a democrat are independent events as the outcome of one does not affect the other.