Question

Suppose the rate of type II diabetes in 40- to 59-year-olds is 7% among Caucasians, 10% among African-Americans, 12% among Hispanics, and 5% among Asian-Americans. Also suppose the ethnic distribution for the age group is 30% Caucasian, 25% African-American, 40% Hispanic, and 5% Asian-American. What is the overall probability of type II diabetes among 40- to 59-year-olds in Houston?

Answer 1

The overall probability of type II diabetes among 40- to 59-year-olds in Houston is 9.3%.

Explanation:

We have these following rates of type II diabetes:

7% among Caucasians

10% among African-Americans

12% among Hispanics

5% among Asian-Americans.

The ethnic distribution of Houston is:

30% Caucasian

25% African-American

40% Hispanic

5% Asian-American

What is the overall probability of type II diabetes among 40- to 59-year-olds in Houston?

`P = P_(1) + P_(2) + P_(3) + P_(4)`

`P_(1)` is the probability of finding a Caucasian with type II diabetes in Houston. So it is 7% of 30%.

`P_(1) = 0.07*0.30 = 0.021`

`P_(2)` is the probability of finding an African-American with type II diabetes in Houston. So it is 10% of 25%.

`P_(2) = 0.1*0.25 = 0.0215`

`P_(3)` is the probability of finding a Hispanic with type II diabetes in Houston. So it is 12% of 40%.

`P_(3) = 0.12*0.40 = 0.048`

`P_(4)` is the probability of finding an Asian-American with type II diabetes in Houston. So it is 5% of 5%.

`P_(3) = 0.05*0.05 = 0.0025`

`P = P_(1) + P_(2) + P_(3) + P_(4) = 0.021 + 0.0215 + 0.048 + 0.0025 = 0.093`

The overall probability of type II diabetes among 40- to 59-year-olds in Houston is 9.3%.