# Examples of Random Numbers

Example:

Two balanced coins are to be tossed 10 times to record the number of heads each time. Use a random number table to record the possible observations. Write the frequency distribution of the observed number of heads.

Solution:

Two digits of a random number table will represent the result of a throw of two coins. We shall take ten pairs of random numbers for 10 throws of two coins.

From the given table we take 10 pairs of random digits and count the number of heads. Even digits will indicate heads (H) and odd digits will indicate tails (T).

 Random pairs: 51 22 09 12 72 12 40 92 72 95 Number of even digits: 0 2 1 1 1 1 2 1 1 0 No. of heads: 0 2 1 1 1 1 2 1 1 0

The observed frequency distribution of number of heads is

 Number of Heads Frequency 0 2 1 6 2 2 Total 10

If two coins are actually tossed 10 times, the observed frequency distribution may or may not agree with the above distribution.

Note: If 3 coins are to be tossed, we shall take 3 digits to represent a throw of 3 coins.

Example:

Assume that a fair die is to be rolled ten times. Without rolling the die, obtain the possible outcomes using random digits.

Solution:

Here the six digits 1, 2, 3, 4, 5, 6 will represent the six faces of the die. We shall ignore the random digit 0 and the digits above 6.

From the above table we have the random digits

5 1  2  2  1  2  2  1  2  4

Thus we assume that the first throw has given 5 on the die, the second throw has given 1 on the die and the 10th throw has given 4 on the die.