Random Number Tables
Using Random Numbers
Rain or Shine?
Two-figure Random Numbers
|
|
Random Numbers
You have used SIMULATIONS to help you see how real problems
may turn out. Chance was involved, so you used cards or a die.
This took a long time, and so here is a quicker method.
You will need page R2.
Random Number Tables
These are the results of throwing a die 30 times.
| 2 |
3 |
2 |
1 |
4 |
5 |
6 |
1 |
3 |
5 |
| 6 |
1 |
2 |
5 |
6 |
3 |
1 |
4 |
3 |
4 |
| 1 |
6 |
4 |
1 |
3 |
4 |
3 |
5 |
6 |
1 |
You could use a table like this in Is there Room on the Bus? instead of throwing a
die. With a whole page of results, you can do a lot of trials
more quickly.
A table with all the digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, can
be produced by a computer. It is called a table Of RANDOM
NUMBERS, because each number from 0 to 9 is equally likely to
happen next. See Table 1 for an example.
| 9 |
1 |
9 |
3 |
8 |
8 |
5 |
6 |
3 |
5 |
| 7 |
6 |
9 |
7 |
3 |
5 |
1 |
9 |
3 |
7 |
| 1 |
4 |
6 |
6 |
0 |
7 |
4 |
6 |
5 |
0 |
| 5 |
8 |
0 |
8 |
7 |
3 |
4 |
2 |
9 |
7 |
| 2 |
0 |
4 |
2 |
6 |
4 |
6 |
8 |
0 |
0 |
Table 1 - Random numbers from 0 to 9
To obtain random numbers.
Rule 1
Start anywhere: touch the random number table and write down
the number nearest your finger.
Rule 2
Move your finger in any direction on the table. Keep it
moving in this direction.
Rule 3
Write down each figure you touch. Do not miss any out.
For example, starting on the second line we get:
7 6 9 7 3
| a |
Write down the next rive random numbers from
the table. |
| b |
Use Table 1 to write down 10 random numbers. |
Using Random Numbers
You will need page R2.
Albert Ward can use random numbers for his minibus problem. On
average, out of every six seats booked one person did not come.
This is a probability of one in six.
He needs six digits: 1, 2, 3, 4, 5 and 6.
If the number is 1, the person does not come.
If the number is 2, 3, 4, 5, 6, the person does come.
If the number is 7, 8, 9, 0, we go to the next number.
Table 1 gives:
9 |
1 |
9 |
3 |
8 |
8 |
5 |
6 |
3 |
5 |
7 |
6 |
9 |
7 |
3 |
5 |
1 |
9 |
3 |
7 |
| 1 |
4 |
6 |
6 |
0 |
7 |
4 |
6 |
5 |
0 |
| 5 |
8 |
0 |
8 |
7 |
3 |
4 |
2 |
9 |
7 |
| 2 |
0 |
4 |
2 |
6 |
4 |
6 |
8 |
0 |
0 |
So a possible list of random numbers is:
1, 3, 5, 6, 3, 5, 6, 3, 5, 1, 3, 1, 4, 6, 6,
The person does not come where the number is underlined.
Using this list of numbers, the results for A3 would begin this
way:
| Trip |
Person Booking |
Total |
Number over booked |
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
| 1 |
 |
 |
|
|
|
|
|
|
|
|
|
|
9 |
|
| 2 |
|
|
|
|
|
|
|
|
|
|
|
|
12 |
2 |
| 3 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
You can see that we would need to have many more random
numbers.
If there is a chance that one person in four will not come, we
need the numbers 1, 2, 3, 4. We say that:
If the number is 1, the person does not come.
If the number is 2, 3, 4, the person does come.
If the number is 5, 6, 7, 8, 9, we go to the next number.
Our random number table gives
9 |
1 |
9 |
3 |
8 |
8 |
5 |
6 |
3 |
5 |
7 |
6 |
9 |
7 |
3 |
5 |
1 |
9 |
3 |
7 |
| 1 |
4 |
6 |
6 |
0 |
7 |
4 |
6 |
5 |
0 |
So we could use the list:
1, 3, 3, 3, 1, 3, 1, 4, 4,....
Use page R2 to show in the same way what you would do if the
probability was:
| a |
1 in 5 (i.e. 1/5) |
| b |
1 in 8 (i.e. 1/8) |
| c |
1 in 10 (i.e. 1/10) |
Rain or Shine?
The Sheffield Weather Summary for 1976 shows that there were
18 rainy days in September. We estimate the probability of a
rainy day in the following September as 18/30, or 3 in 5.
To simulate the weather we need the numbers 1,2,3,4,5. We say
that:
If the number is 1,2,3, it rains.
If the number is 4, 5, it will be dry.
If the number is 0, 6, 7, 8, 9, we go to the next number.
A possible list of random numbers is:
1, 3, 5, 3, 5, 3, 5, 1, 3, 1, 4, 4, 5, 5, 3, 4, 2, 2, 4, 2, 4 ...
The rainy days are underlined. So in the first week there are
four rainy days.
Write down a similar method if the probability of rain
is:
| a |
2 in 5 (i.e. 2/5) |
| b |
4 in 7 (i.e. 4/7) |
| c |
3 in 8 (i.e. 3/8) |
| d |
3 in 10 (i.e. 3/10) |
Two-figure Random Numbers
If we need bigger random numbers we must read from the table
two digits at a time. Starting on the second line of Table 1 we
get:
76, 97, 35, 19, 37, 14, 66, 07, 46, 50, ...
If we need to simulate a probability of 7 in 60, we could say
that:
If the number is 01, 02, 03, 04, 05, 06, 07, it happens.
If the number is 08, 09, 10, ....... 59, 60, it does not happen.
If the number is 61, 62, ....... 98, 99, 00, we go to the next
number.
So our list becomes 35, 19, 37, 14, 07, 46, 50, ...
The event happens on the fifth trial.
| a |
Write down 20 two-digit random
numbers from page R4. |
Which of these would you use for a probability of:
| a |
7 in 30 (i.e. 7/30
) |
| b |
11 in 70 (i.e. 11/70) |
| c |
1 in 13 (i.e. 1/13) |
| d |
In each list underline the
numbers which show that the event takes place. |
|
