Chapter 5.1, Problem 19E

(a)

To determine

To state the question of interest using the language of probability.

Explanation of Solution

By looking at the question, the question of interest made using the language of probability is as follows:

What is the probability that out of $12$ first class passengers and $64$ coach class passengers, a random screening of $10$ passengers would include none from first class?

This is the question stated using the language of probability.

(b)

To determine

To explain how would you use random digits to imitate one repetition of the process and find out what variable you would measure.

Answer to Problem 19E

The variable measured is the number of first class passengers.

Explanation of Solution

To use random digits to imitate one repetition of the process, we will do as;

As we know that numbers $01-12$ could represent the first class passengers and $13-76$ could represent coach class passengers. Ten two-digit numbers could then be taken from a line of the random digits table, skipping over repeated numbers and those from $77-100$ . Then the number of first class passengers in the selection could be measured.

Thus the variable measured is the number of first class passengers.

(c)

To determine

To use the line of random digits given to perform one repetition and explain the process.

Explanation of Solution

As in the question given the random digits as-

  $71487,09984,29077,14863,61683,47052,62224,51025$ .

Select the first two digit number. If the number is between $01\text{ and 76}$ , then select the correspond passenger, else ignore the number and move on to the next two digit number.

This is explained as,

  $\begin{array}{l}71\Rightarrow \text{Select passenger71}\\ \text{48}\Rightarrow \text{Select passenger48}\\ 70\Rightarrow \text{Select passenger70}\\ 99\Rightarrow \text{Ignore}\\ \text{84}\Rightarrow \text{Ignore}\\ \text{29}\Rightarrow \text{Select passenger29}\\ 07\Rightarrow \text{Select passenger07}\\ 71\Rightarrow \text{Repeated thus ignore}\\ 48\Rightarrow \text{Repeated thus ignore}\\ 63\Rightarrow \text{Select passenger63}\\ 61\Rightarrow \text{Select passenger61}\\ 68\Rightarrow \text{Select passenger68}\\ 34\Rightarrow \text{Select passenger34}\\ 70\Rightarrow \text{Repeated thus ignore}\\ 52\Rightarrow \text{Select passenger52}\end{array}$

Thus the numbers selected are as:

  $71,48,70,29,07,63,61,68,34,52$ .

(d)

To determine

To explain what conclusion would you draw.

Explanation of Solution

As we know that numbers $01-12$ could represent the first class passengers and $13-76$ could represent coach class passengers. Ten two-digit numbers could then be taken from a line of the random digits table, skipping over repeated numbers and those from $77-100$ , then first class passengers could be measured.

Thus when in $100$ repetitions of the simulation, there were $15$ times when none of the ten passengers chosen were seated in first class. This may conclude that the ten passengers chosen could have the numbers between $13-76$ that represents coach class passengers or from $77-100$ that are skipped. This can happen as ten numbers are randomly chosen.