Choose a young adult (age 25 to 34 years) at random. The probability is 0.20 tha
ID: 3204951 • Letter: C
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 0.25 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
ans=
P(No H.S.) = 0.20
P(H.S. only) = 0.32
P(Bachelors or more) = 0.25
This is a type of problem that you need to play with the wording until it is clear that the statements made create disjoint statements. One group does not finish high school, while another only finishes high school, which is different from those that finished high school and attained at least a bachelors.
A) Notice the shaded area depicts someone that has a high school diploma but not a bachelors or higher degree, yet it is not only a high school degree.
1 – (0.20 + 0.32 + 0.25) = 0.23
B) Notice that this statement includes everyone except those that did not attain a high school diploma.
P(at least HS) = 1 – P(no HS) = 1 – 0.20 = 0.80