Use Bayes' theorem to find the indicated probability.
-Use the results summarized in the table. $$\begin{array} { l | c c }
& \text { Approve of mayor } & \text { Do not approve of mayor } \
\hline \text { Republican } & 15 & 13 \
\text { Democrat } & 20 & 17 \
\text { Independent } & 12 & 23
\end{array}$$
One of the 100 test subjects is selected at random. Given that the person selected approves of the mayor, what is the probability that they vote Democrat?
A) 0.313
B) 0.578
C) 0.426
D) 0.541

Question

Use Bayes' theorem to find the indicated probability.
-Use the results summarized in the table. $$\begin{array} { l | c c } 
& \text { Approve of mayor } & \text { Do not approve of mayor } \
\hline \text { Republican } & 15 & 13 \
\text { Democrat } & 20 & 17 \
\text { Independent } & 12 & 23
\end{array}$$
 One of the 100 test subjects is selected at random. Given that the person selected approves of the mayor, what is the probability that they vote Democrat?
A) 0.313
B) 0.578
C) 0.426
D) 0.541

Quizplus · Accepted Answer

The probability that a person approves of the mayor and is a Democrat is 20/100. The probability that a person approves of the mayor is (15+20+12)/100 = 47/100. Using Bayes' theorem, the probability that a person is a Democrat given they approve of the mayor is (20/100) / (47/100) = 20/47 ≈ 0.426.

Use Bayes' Theorem to Find the Indicated Probability One of the 100 Test Subjects Is Selected at Random