Chapter 11, Problem 23E

To determine

To find: the proportion of the time to win on the basis of given information.

Explanation of Solution

Step 1

There is the lottery number details picked as the last to draw the lottery recently, so watch the lottery to record the winning number to try the "rarest" value to win the lottery.

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

Supposing, from the single digits random number 0-9, we bet on the 7 number randomly and there is required to win the lottery, so there is required to run at least 100 trials to see how many times we win the lottery.

Randomly, pick a winning number and we take 100 tests. By using random number generators, it produces 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	7	4	4
5	7	7	5	5
2	7	8	8	5
6	6	7	6	8
8	8	5	2	9
4	7	7	3	0
6	7	6	6	1
5	9	8	1	5
8	1	4	3	1
7	8	8	8	4
2	1	7	6	2
7	0	5	5	4
7	5	4	1	6
5	1	4	7	4
8	7	3	4	8
8	9	5	1	9
5	7	7	5	7
4	7	4	4	4
4	7	5	7	5
8	8	7	7	8

 Step 2

The result of the number 7 trials is 10 to win the lottery.

Step 3

The proportion of the time is

  $\begin{array}{c}lottery=\frac{totalnumberofchance\text{}towin1number}{totalnumberoftrials}\\ =\frac{10}{100}\times 100\\ =10\%\end{array}$

The proportion of the amount of time it is intended to win is 10%.

Step4

Based on simulation, it can infer that if play lottery numbers turn up least in recent drawers, then it should also win the lottery around 10% of the time so that there is no gain in recent drawer lottery to play the turn up least because each new lottery drawing is independent of recent drawing.