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.

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.