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
female	13	32	19	19	83
total	29	61	38	35	163

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

Explanation:

Step1: Recall the formula for odds in - favor

The odds in favor of an event $E$ is given by $\frac{P(E)}{1 - P(E)}=\frac{n(E)}{n(\text{not }E)}$, where $n(E)$ is the number of favorable outcomes and $n(\text{not }E)$ is the number of non - favorable outcomes. The number of people with four years (or more) of college is $n(E)=35$ million, and the number of people without four years (or more) of college is $n(\text{not }E)=163 - 35=128$ million.

Step2: Calculate the odds in favor

The odds in favor of selecting a member of the population with four years (or more) of college is $\frac{n(E)}{n(\text{not }E)}=\frac{35}{128}$.

Step3: Calculate the odds against

The odds against an event $E$ is given by $\frac{1 - P(E)}{P(E)}=\frac{n(\text{not }E)}{n(E)}$. So the odds against selecting a member of the population with four years (or more) of college is $\frac{128}{35}$.

Answer:

The odds in favor are $\frac{35}{128}$.
The odds against are $\frac{128}{35}$.