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	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 16 : 41 .
(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 \\(\square:\square\\).
(simplify your answers.)

Explanation:

Step1: Recall the formula for odds against

Odds against an event \(E\) is given by \(\text{Odds against }E=\frac{\text{Number of unfavorable outcomes}}{\text{Number of favorable outcomes}}\)

The number of favorable outcomes (with 4 years or more of college) is \(n(F) = 48\) (from the table). The number of unfavorable outcomes (not with 4 years or more of college) is \(n(U)=171 - 48=123\)

Step2: Calculate the odds against

\(\text{Odds against}=\frac{n(U)}{n(F)}=\frac{123}{48}\)

Simplify the fraction \(\frac{123}{48}\) by dividing numerator and denominator by 3. \(\frac{123\div3}{48\div3}=\frac{41}{16}\)

Answer:

\(41:16\)