Choose a young adult (age 25 to 34 years) at random. The probability is 0.20 tha

Question

Choose a young adult (age 25 to 34 years) at random. The probability is 0.20 that the person chosen did not complete high school, 0.32 that the person has a high school diploma but no further education, and 0.31 that the person has at least a bachelor's degree.

(a) What must be the probability that a randomly chosen young adult has some education beyond high school but does not have a bachelor's degree?
(b) What is the probability that a randomly chosen young adult has at least a high school education?

Explanation / Answer

The probabilities for E, the person's level of education, are:
E < high school: 0.2
E = high school: 0.32
E >= degree (bachelor's or higher): 0.31

I've put these in symbolic terms so you can see what's missing. These probabilities add up to 0.83, which means that the probability that
high school < E < degree (bachelor's or higher)
must account for the missing portion:
1 - 0.83 = 0.17 = 17%

This is the answer to part a, and includes associate degrees and college education with no degree.

It's common to expres probabilities as fractions or decimals (0.17 in this case). A percentage (17%) in this case is numerically equivalent, but better avoided unless the problem was stated in terms of percentages in the first place.

b) The easiest way to get this is to subtract from 1 (certainty) the probability that the person did not complete high school:
1 - 0.2 = 0.8

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