A probability distribution table is a table that shows the probabilities of occurrence of an event in tabular form corresponding to the value of the random variable.

**Example:**

Suppose that a die is thrown. Let X denote the number that occurs on the uppermost face of the dice. Then X is a random variable since we cannot predict what number will occur on the die in advance. Each of the numbers 1,2,3,4,5 and 6 has a one out of six chance of occurring. The probability distribution table looks like,

Random Variable X | Probability P(X) |

1 | 1/6 |

2 | 1/6 |

3 | 1/6 |

4 | 1/6 |

5 | 1/6 |

6 | 1/6 |

Notice that the sum of all the probabilities in our table adds up to 1. This is true in general and in fact, this property can be used to complete a probability distribution table.

**How to complete a probability distribution table?**

In order to find the missing value in a probability distribution table, we make use of the fact that the sum of all the probabilities should add up to 1. Consider the following incomplete distribution table,

Random Variable X | Probability P(X) |

1 | 0.1 |

2 | ? |

3 | 0.2 |

4 | 0.3 |

Let the unknown probability value be a. We have that,

P(X=1) + P(X=2) + P(X=3) + P(X=4) = 1 0.1 + a + 0.2 + 0.3 = 1 \implies 0.6 + a = 1 \implies a = 0.4So the completed probability table looks like,

Random Variable X | Probability P(X) |

1 | 0.1 |

2 | 0.4 |

3 | 0.2 |

4 | 0.3 |