11. Among adults over age 25 in the U.S., 87.6 percent graduated from high schoo
ID: 3350436 • Letter: 1
Question
11. Among adults over age 25 in the U.S., 87.6 percent graduated from high school, 35.3 percent of high school graduates earned a bachelor's degree, and 5 percent of people with a bachelor's degree also earned a Ph.D. (You may assume that everyone with a bachelor's degree graduated from high school, and everyone with a Ph.D. has a bachelor's degree.) (a) What percentage of people over age 25 in the U.S. have earned a Ph.D.? (b) If a person over age 25 is chosen at random, what is the conditional probability that the person earned a Ph.D. given that the person graduated from high schoolExplanation / Answer
Let A denote the event of graduating from high school, B denote the event of earning a bachelor's degree and C denote the event of earning a Ph.D.
Given P(A) = 0.876 P(B|A) = 0.353 P(C|B) = 0.05
(a) P(B) = P(A and B) = P(A) P(B|A) = 0.876 * 0.353
P(C) = P(B and C) = P(B) P(C|B) = 0.876 * 0.353 * 0.05 = 0.0154614 = 1.55%.
(b) P(C|A) = P(C and A) / P(A) = P(C) / P(A) = 0.0154614 / 0.876 = 0.01765.
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