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# Doctorates Conferred The following probability model shows the distribution of doctoral degrees from U.S. universities in 2009 by area of study.

Doctorates Conferred The following probability model shows the distribution of doctoral degrees from U.S. universities in 2009 by area of study.

Area of Study
Probability
Engineering
0.154
Physical sciences
0.087
Life sciences
0.203
Mathematics
0.031
Computer sciences
0.033
Social sciences
0.168
Humanities
0.094
Education
0.132
Professional and other fields
0.056
Health
0.042
Source: U.S. National Science Foundation
(a) Verify that this is a probability model.
(b) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 studied physical science or life science? Interpret this probability.
(c) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 studied physical science, life science, mathematics, or computer science? Interpret this probability.
(d) What is the probability that a randomly selected doctoral candidate who earned a degree in 2009 did not study mathematics? Interpret this probability.