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	15	32	25	21	93
total	27	63	49	46	185

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 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 \(\frac{\text{Number of favorable outcomes}}{\text{Number of non - favorable outcomes}}\). The number of people with four years (or more) of college is \(46\) (from the table), and the number of people without four years (or more) of college is \(185 - 46=139\).
So, the odds in favor of selecting a member with four years (or more) of college is \(\frac{46}{139}\).

Step2: Recall the formula for odds against

The odds against an event \(E\) is given by \(\frac{\text{Number of non - favorable outcomes}}{\text{Number of favorable outcomes}}\).
So, the odds against selecting a member with four years (or more) of college is \(\frac{139}{46}\).

Answer:

The odds in favor: \(\frac{46}{139}\)
The odds against: \(\frac{139}{46}\)