# 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.