Use Bayes's Rule to Find the Indicated Probability An Adult Is Picked at Random from the City

Multiple Choice

Use Bayes's rule to find the indicated probability.
-The first two columns of the table below give a percentage distribution for adults in one city by income group. The third column gives the percentage of people in each income group who plan to Buy a new car next year. $$\begin{array} { c c c } \begin{array} { l } \text { Income } \\\text { (dollars) }\end{array} & \begin{array} { c } \text { Percentage } \\\text { of population }\end{array} & \begin{array} { c } \text { Percentage that will } \\\text { buy new car next year }\end{array} \\\hline 0 - 4999 & 5.2 & 2 \\5000 - 9999 & 6.4 & 3 \\10,000 - 14,999 & 5.4 & 6 \\15,000 - 19,999 & 8.7 & 7 \\20,000 - 24,999 & 9.4 & 9 \\25,000 - 29,999 & 10.2 & 10 \\30,000 - 34,999 & 13.8 & 11 \\35,000 - 39,999 & 10.7 & 13 \\40,000 - 49,999 & 15.5 & 15 \\50,000 \text { and over } & 14.7 & 19\end{array}$$ An adult is picked at random from the city. Given that the person selected plans to buy a new car Next year, what is the probability that the person's income is between $5,000 and $9,999?

A) 0.05
B) 0.03
C) 0.01
D) 0.02