Question

In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Graduate Science Students. According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows.

Frequencies are in thousands. Note: Earth sciences include atmospheric and ocean sciences as well.

A graduate science student who is attending a doctorate-granting institution is selected at random. Determine the probability that the field of the student obtained is

(a) psychology.

(b) physical or social science.

(c) not computer science.

Short answer

Part (a) 0.131.

Part (b) 0.389.

Part (c) 0.868.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

According to the Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows.

Frequencies are in the thousands.

Field	Frequency (in thousands)
Agricultural Sciences	15.1
Biological Sciences	69.7
Computer Sciences	46.1
Earth Sciences	14.9
Mathematical Sciences	22.0
Physical Sciences	38.7
Psychology	45.6
Social Sciences	97.2

Part (a) Step 2. Find the probability that the field of the obtained student is psychology.

We know that an event's probability ranges from 0 to 1, and both 0 and 1 are included in it.

The formula for the probability of an event is:

$P\left(E\right)=\frac{No.offavorableoutcomes}{Totalno.ofoutcomes}$

The total number of graduate science students in doctorate-granting institutions is 349.3 thousand.

The total number of instances where the selected student is from psychology is 45.6 thousand.

Now Let's take the occurrence 'E' as the selected student is from psychology.

The probability that the selected student is from psychology:

$$\begin{gathered} P\left(E\right)=\frac{45.6}{349.3} \\ =0.131 \end{gathered}$$

Part (b) Step 1. Find the probability that the field of the obtained student is physical or social science.

The total number of instances where the selected student is from physical or social science:

$45.6+97.2=135.9\mathrm{thousand}$

Now Let's take the occurrence 'E' as the selected is from physical or social science.

The probability that the selected student is from physical or social science:

$$\begin{gathered} P\left(E\right)=\frac{135.9}{349.3} \\ =0.389 \end{gathered}$$

Part (c) Step 1. Find the probability that the field of the obtained student is not computer science.

The total number of instances where the selected student is not from computer science.

$$\begin{gathered} \mathrm{Total}\mathrm{students}-\mathrm{students}\mathrm{from}\mathrm{computer}\mathrm{science} \\ =349.3-46.1 \\ =303.2 \end{gathered}$$

Now Let's take the occurrence 'E' as the selected student is not from computer science.

The probability that the selected student is not from computer science:

$$\begin{gathered} P\left(E\right)=\frac{303.2}{349.3} \\ =0.868 \end{gathered}$$