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.
male female total
less than 4 years high school 13 13 26
4 years high school only 31 24 55
some college (less than 4 years) 19 20 39
4 years college (or more) 21 17 38
total 84 74 158
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.)

Explanation:

Step1: Identify favorable and non - favorable outcomes

The number of people with four years (or more) of college is the sum of those with 4 years College (or More), which is \(21 + 17=38\). The number of people without four years (or more) of college is the total population minus the number of people with four years (or more) of college. The total population is 158. So the number of people without four years (or more) of college is \(158 - 38 = 120\).

Step2: Calculate odds in favor

The odds in favor of an event \(E\) is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. So the odds in favor of selecting a person with four years (or more) of college is \(\frac{38}{120}=\frac{19}{60}\).

Step3: Calculate odds against

The odds against an event \(E\) is the ratio of the number of non - favorable outcomes to the number of favorable outcomes. So the odds against selecting a person with four years (or more) of college is \(\frac{120}{38}=\frac{60}{19}\).

Answer:

Odds in favor: \(\frac{19}{60}\)
Odds against: \(\frac{60}{19}\)