Chapter 17, Problem 3E

(a)

To determine

To Explain: using random numbers will model the search for Tiger wood picture.

Explanation of Solution

Please number all of the cereal boxes. Pick up some random number and pick up the random number of the cereal box and check if there is an image of Tiger Wood. Until get a picture, continue this process. In order to obtain the first tiger wood image, remember the number of boxes opened. Again, repeat the procedure.

(b)

To determine

To conduct: the 30 trials to search the picture of tiger woods.

Explanation of Solution

Following it the numbers of boxes opened to find the first tiger wood image is given after the number.

5, 2, 5, 4, 8, 6, 3, 8, 9, 4, 7, 6, 2, 5, 1, 2, 10, 8, 4, 8, 5, 5, 6, 4, 7, 8, 9, 10, 2, 9

(c)

To determine

To Calculate: the probability on the basis given simulation which may get the 1^st picture of Tiger wood in the 1^st box, 2^nd etc.

Explanation of Solution

The probability of opening X boxes to find the image in the first box is computed by counting the X number in the table above it and dividing this by 30.

Number of boxes open to Find the 1st image	Number of times	$P\left(X\right)$
1	1	0.033
2	4	0.133
3	1	0.033
4	4	0.133
5	5	0.167
6	3	0.1
7	2	0.067
8	5	0.167
9	3	0.1
10	2	0.067

(d)

To determine

To find: the actual probability.

Explanation of Solution

This table is giving the actual probability

Number of box open to finding the 1st picture	$P\left(X\right)$
1	0.2
2	0.16
3	0.128
4	0.1024
5	0.0819
6	0.0655
7	0.0524
8	0.0419
9	0.0336
10	0.0268

(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.