Chapter 15, Problem 19E

(a)

To determine

To find: the percent of the junior Biology majors are ineligible for Bioresearch.

Answer to Problem 19E

0.32

Explanation of Solution

Given:

  $\begin{array}{c}P\left(S\right)=0.52\\ P\left(C\right)=0.23\\ P\left(S\cap C\right)=0.07\end{array}$

Formula used:

  $P\left(S\text{'}\cap C\text{'}\right)=1-P\left(S\cup C\right)$

Calculation:

Junior Biology Majors are ineligible if they have taken neither Statistic nor Computer course. Then calculate this using complements.

  $\begin{array}{c}P\left(S\text{'}\cap C\text{'}\right)=1-P\left(S\cup C\right)\\ =1-\{P\left(S\right)+P\left(C\right)-P\left(S\cap C\right)\\ =1-\{0.52+0.23-0.07\}\\ =1-0.68\\ =0.32\end{array}$

About 32% of Biology majors are ineligible.

(b)

To determine

To find: the probability that a junior Biology major that taken Statistics has taken a computer course.

Answer to Problem 19E

0.1346

Explanation of Solution

Formula used:

  $P\left(C|S\right)=\frac{P\left(C\cap S\right)}{P\left(S\right)}$

Calculation:

Probability that junior Biology major who has taken statistics has also taken a computer science is

  $\begin{array}{c}P\left(C|S\right)=\frac{P\left(C\cap S\right)}{P\left(S\right)}\\ =\frac{0.07}{0.52}\\ =0.1346\end{array}$

There is 13.5% possibility that junior biology major who has taken statistics has also taken a computer science.

(c)

To determine

To Explain: about these two courses disjoint events.

Answer to Problem 19E

Not disjoint

Explanation of Solution

Although $P\left(C\cap S\right)\ne 0$ therefore they are not disjoint

(d)

To determine

To Explain: about these two courses independent events.

Answer to Problem 19E

Not independent

Explanation of Solution

Formula used:

  $P\left(C|S\right)=\frac{P\left(C\cap S\right)}{P\left(S\right)}$

Calculation:

Test for independency.

For this

  $\begin{array}{c}P\left(C|S\right)=\frac{P\left(C\cap S\right)}{P\left(S\right)}\\ =\frac{0.07}{0.52}\\ =0.1346\\ P\left(C\right)=0.23\\ P\left(C|S\right)\ne P\left(C\right)\end{array}$

Therefore they are not independent