Question

the table shows the educational attainment of a population, expressed in millions. find the odds in favor and the odds against a randomly selected member of the population with four years (or more) 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	13	31	18	23	85
female	14	27	20	25	86
total	27	58	38	48	171

the odds, in most reduced form, in favor of selecting a member of the population with four years (or more) of college are \\(\square:\square\\).
(simplify your answers.)

Explanation:

Step1: Calculate the number of favorable and unfavorable outcomes

The number of people with 4 years (or more) of college is \(n(F) = 48\) (from the table).
The number of people without 4 years (or more) of college is \(n(U)=27 + 58+38=123\).

Step2: Calculate the odds in favor

The formula for odds in favor is \(\text{Odds in favor}=\frac{n(F)}{n(U)}\).
Substitute \(n(F) = 48\) and \(n(U)=123\) into the formula: \(\frac{48}{123}=\frac{16}{41}\) (divide numerator and denominator by 3).

Answer:

\(16:41\)