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
4 years high school only	30	25	55
some college (less than 4 years)	25	18	43
4 years college (or more)	25	21	46
total	93	78	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 people with four years (or more) of college

From the table, the total number of people with four years (or more) of college (the "More" row) is \(46\) million.

Step2: Calculate the number of people without four years (or more) of college

The total population is \(171\) million. The number of people without four years (or more) of college is \(171 - 46=125\) million.

Step3: Calculate the odds in favor

The odds in favor of an event \(E\) (selecting a person with four years (or more) of college) is given by \(\frac{n(E)}{n(\text{not }E)}\), where \(n(E)\) is the number of favorable outcomes and \(n(\text{not }E)\) is the number of unfavorable outcomes. So, the odds in favor is \(\frac{46}{125}\).

Step4: Calculate the odds against

The odds against an event \(E\) is \(\frac{n(\text{not }E)}{n(E)}\), so the odds against is \(\frac{125}{46}\).

Answer:

The odds in favor are \(\frac{46}{125}\) and the odds against are \(\frac{125}{46}\)