Chapter 11, Problem 22E

To determine

To find: the proportion of the time to win.

Explanation of Solution

Step 1

There are random lottery number results, so it is easier to randomly pick the number to win the lottery.

The proportion of the time that we intend to win is as follows:

Supposing, from the single digits random number 0-9, we bet on the 5 number randomly and there is required to win the lottery, so it is needed to run at least 100 trials to see how many times we win the lottery.

Randomly, pick a winning number and take 100 tests. By using random number generators, we produce random numbers using the following steps:

1) Add random numbers as per our maximum requirement of 1000.

2) Depending on random numbers, between 0 and 9

3) Press the Submit key.

1	5	8	7	4
5	4	4	5	5
2	5	8	6	4
6	6	9	6	6
8	8	5	8	8
4	8	7	4	0
6	1	6	6	1
5	9	5	1	5
8	1	5	8	1
8	8	8	8	8
2	1	7	9	2
5	0	5	5	8
5	5	5	1	8
5	1	4	7	8
8	4	7	4	8
6	9	5	1	8
5	8	5	7	7
4	6	4	4	7
5	8	5	7	5
8	8	7	8	8

Step 2

The result is 10 trials for number 5 to win the lottery.

Step 3

The proportion of the time that we intend to win is as follows:

  $\begin{array}{c}Randomneeslottery=\frac{totalnumberofwin1number}{totalnumberoftrials}\\ =\frac{10}{100}\times 100\\ =10\%\end{array}$

The amount of time intends to win is 10%.

Step 4

Based on simulation, it can infer that if we randomly play lottery numbers, it can also win the lottery about 10% of the time, so there is no value in randomly selecting the lottery number.