Chapter 17, Problem 4E

(a)

To determine

To Explain: would simulate the rolling the die till obtain a 1.

Explanation of Solution

Rolling a die till get 1. Counting the number of times rolled, repeating the roll from the 1^st time again.

(b)

To determine

To conduct: minimum the 30 trials to get 1.

Explanation of Solution

Below provides the number of times a die is rolling to get 1

6, 9, 10, 9, 4, 9, 10, 7, 6, 9, 12, 18, 20, 12, 2, 1, 20, 20, 6, 9, 8, 10, 10, 5, 8, 10, 8, 6, 3, 7

(c)

To determine

To Calculate: the probability on the basis given simulation which may get the 1^st roll, 2^nd roll etc.

Explanation of Solution

The chance that the number of times a die is rolling to get 1 is achieved by counting and dividing the number of 1's and in table above by 30

Number of times die Is rolled to obtained 1	Number of times occurred	$P\left(X\right)$
1	1	0.0333
2	1	0.0333
3	1	0.0333
4	1	0.0333
5	1	0.0333
6	4	0.1333
7	2	0.0667
8	3	0.1
9	5	0.1667
10	5	0.1667
12	2	0.0667
18	1	0.0333
20	3	0.1

(d)

To determine

To find: the actual probability.

Explanation of Solution

Following table mention the actual probability model.

  $P\left(X=x\right)={\left(\frac{5}{6}\right)}^{x-1}\left(\frac{1}{6}\right)$

	$P\left(X\right)$
1	$\frac{1}{6}$
2	$\left(\frac{5}{6}\right)\left(\frac{1}{6}\right)=0.139$
3	${\left(\frac{5}{6}\right)}^2\left(\frac{1}{6}\right)=0.116$
4	${\left(\frac{5}{6}\right)}^3\left(\frac{1}{6}\right)=0.0965$
5	${\left(\frac{5}{6}\right)}^4\left(\frac{1}{6}\right)=0.0804$
6	${\left(\frac{5}{6}\right)}^5\left(\frac{1}{6}\right)=0.0670$
7	${\left(\frac{5}{6}\right)}^6\left(\frac{1}{6}\right)=0.0558$
8	….

(e)

To determine

To Explain: the comparison the distribution of the results with the simulation to the probability.

Explanation of Solution

By seeing the both the table, it is observed that the real probability is not similar at all, it raises the number of trials it may be similar to.