# Question

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

(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.

(e) Are doctoral degrees in mathematics unusual? Does this result surprise you?

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

(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.

(e) Are doctoral degrees in mathematics unusual? Does this result surprise you?

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