Question

the table below shows the educational attainment of a countrys population, aged 25 and over. use the data in the table, expressed in millions, to find the probability that a randomly selected citizen, aged 25 or over, had 4 years of college. \
\

	less than 4 years high school	4 years high school only	some college (less than 4 years)	4 years college (or more)	total	\
---	---	---	---	---	---	\
male	12	22	17	21	72	\
female	18	24	26	19	87	\
total	30	46	43	40	159	\

\
the probability that a randomly selected citizen, aged 25 or over, had 4 years of college is \
(type an integer or a simplified fraction.)

Explanation:

Step1: Identify relevant data

We need the number of citizens with 4 years of college (or more) and the total number of citizens aged 25 or over. From the table, the number of citizens with 4 years of college (or more) is 40 (from the "Total" row and "4 Years College (or More)" column), and the total number of citizens is 159 (from the "Total" row and "Total" column).

Step2: Calculate probability

Probability is the number of favorable outcomes (citizens with 4 years of college) divided by the number of total outcomes (total citizens). So the probability is $\frac{40}{159}$. Wait, no, wait. Wait, the "4 Years College (or More)" total is 40, and total population is 159? Wait, no, let's check the table again. Wait, the "Total" row: "4 Years College (or More)" is 21 (male) + 19 (female) = 40. Total population is 72 (male total) + 87 (female total) = 159. So probability is number of 4 years college (or more) divided by total population. So that's $\frac{40}{159}$? Wait, but let's check the table again. Wait, the "Total" column for "4 Years College (or More)" is 40, and total population is 159. So yes, probability is $\frac{40}{159}$? Wait, but maybe I made a mistake. Wait, no, the problem says "had 4 years of college", which is "4 Years College (or More)"? Wait, the table has "4 Years College (or More)" as a category. So the number of people with 4 years of college (or more) is 40, total population is 159. So the probability is $\frac{40}{159}$? Wait, but let's check the numbers again. Male with 4 years college: 21, female: 19, so total 21 + 19 = 40. Total population: 72 + 87 = 159. So yes, probability is $\frac{40}{159}$. Wait, but can this be simplified? 40 and 159: 159 divided by 3 is 53, 40 divided by 3 is not integer. 40 and 159 have no common factors (since 159 = 3×53, 40 = 2^3×5; no common prime factors). So the probability is $\frac{40}{159}$? Wait, no, wait, maybe I misread the table. Wait, the "4 Years College (or More)" column: male is 21, female is 19, total 40. Total population: 72 (male total) + 87 (female total) = 159. So yes, probability is 40/159. Wait, but let me check again. Wait, the table:

Male: Less Than 4 Years High School:12, 4 Years High School Only:22, Some College (Less Than 4 Years):17, 4 Years College (or More):21, Total:12+22+17+21=72. Correct.

Female: 18+24+26+19=87. Correct.

Total: 30 (Less Than 4 Years High School:12+18), 46 (4 Years High School Only:22+24), 43 (Some College:17+26), 40 (4 Years College:21+19), Total:30+46+43+40=159. Correct.

So the number of people with 4 years of college (or more) is 40, total population is 159. So probability is 40/159. Wait, but the problem says "had 4 years of college" – is "4 Years College (or More)" the same as "had 4 years of college"? The table's category is "4 Years College (or More)", so that includes those with 4 years or more, so that's the group we need. So the probability is 40/159. Wait, but let me check if 40 and 159 can be simplified. 159 ÷ 3 = 53, 40 ÷ 3 is not an integer. 53 is a prime number. 40 and 53 have no common factors. So 40/159 is simplified. Wait, but wait, maybe I made a mistake in the total. Wait, total population is 159, correct. Number of 4 years college: 40, correct. So probability is 40/159. Wait, but let me check again. Wait, the problem says "had 4 years of college" – maybe it's just 4 years, not "or more"? But the table doesn't have a "4 years exactly" category. The categories are "Less Than 4 Years High School", "4 Years High School Only", "Some College (Less Than 4 Years)", "4 Years College (or More)". So "4 Years College (or More)" is the category for those with at least 4 years of college, which would include those with 4 years. So we have to use that. So the number is 40, total is 159. So probability is 40/159. Wait, but let me check the numbers again. Male: 21, female:19, total 40. Total population: 72 + 87 = 159. So yes, 40/159.

Wait, but maybe I made a mistake. Wait, the "Total" row for "4 Years College (or More)" is 40, and total population is 159. So probability is 40/159. So that's the answer.

Answer:

$\frac{40}{159}$