So essentially, a **probability distribution** is a form of representation that tells us the probability for all the possible values of X. It could be any of the following

- A table

- A chart

- An equation

P(x) = x/21

(for x = 1, 2, 3, 4, 5 and 6)

Hence, in a valid, complete probability distribution, there are no negative values, and all the probability values add up to 1. These two conclusions follow from the basic definition of probability.

Also, recall that we discussed that the probability distribution and frequency distribution would be similar in shape, just with different scales. You can try it out in this interactive app. The graph on the left shows the frequency distribution, and the one on the right shows the probability distribution.

Now, let’s say that a company’s management is contemplating investing in a certain project. Before doing this, it wants to use probability to find whether it can safely expect to make a profit. Whether the company makes a profit or not will actually depend on which economic cycle is going on, i.e., recession, boom, and so on.

Based on the opinions of some experts, the following table is created.

Economic Cycle | Probability |

Recession | 0.1 |

Normal | 0.7 |

Boom | 0.2 |

Suppose as an analyst in the investment division, you have been asked to find the answer to the question: “Can the company expect to make a profit or not? Should it invest in this project?”

However, in this form, the table is of no help at all. Hence, let’s quantify it using a random variable. Since you are interested in whether the company will profit or not, let’s define X as the net revenue of the project.

Now, through some calculations, a fellow analyst of the company has arrived at the net revenue for each of these scenarios. She creates a probability distribution with this data

X (Net Revenue of Project, in ₹ crore) | P(x) |

-305 | 0.1 |

+15 | 0.7 |

+95 | 0.2 |

Now, you finally have a probability distribution for X, the net revenue of the project. Using this probability distribution, you can find the answer to our original question: “Can the company expect a profit from this project? Or, should it expect a loss?”. However, to answer this, you will have to learn the concept of expected value, which is what we will cover next.