Chapter 5.1, Problem 20E

(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 of selecting $7$ vowels, from a bag containing $42$ vowels out of $100$ tiles, when you select exactly $7$ tiles?

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 20E

The variable measured is the number of vowels.

Explanation of Solution

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

Use two digits numbers.

If the number is between $00\text{ and 41}$ , then the tile contains a vowel.

If the number is between $42\text{ and 99}$ , then the tile is not a vowel.

Randomly choose $7$ random two digit numbers without replacement, thus without repetition of numbers.

Then count the number of vowels that you have among the $7$ numbers/tiles.

Thus the variable measured is the number of vowels.

(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-

  $00694,05977,19664,65441,20903,62371,22725,53340$ .

Select the first two digit number. If the number is between $00\text{ and 41}$ , then the number correspond a vowel, else the number is not a vowel. Repeated numbers should be ignored.

This is explained as,

  $\begin{array}{l}00\Rightarrow \text{Vowel}\\ \text{69}\Rightarrow \text{No Vowel}\\ 40\Rightarrow \text{Vowel}\\ 59\Rightarrow \text{No Vowel}\\ 77\Rightarrow \text{No Vowel}\\ 19\Rightarrow \text{Vowel}\end{array}$

Thus the numbers selected as vowels are three as:

  $\text{00,40,19}$ .

(d)

To determine

To explain what conclusion would you draw.

Explanation of Solution

As we know that If the number is between $00\text{ and 41}$ , then the tile contains a vowel.

If the number is between $42\text{ and 99}$ , then the tile is not a vowel.

Thus given two times when all $7$ tiles were vowels in $\text{1000}$ repetitions:

  $\begin{array}{l}\frac{2}{1000}=0.002\\ =0.2\%\end{array}$

Since the percentage is below $5\%$ , it is unlikely to draw $7$ vowels.

Hence the conclusion.