The concept of probability is as important as it is misunderstood. It is vital to have a clear understanding of the nature of ‘chance’ in business in order to make well-informed and effective decisions as a manager.

Let’s hear from Thomas about some instances where we encounter probabilities in business as well as in everyday life.

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In the video, you learnt what probability is and some cases where probability is used.

Probability is a measure of uncertainty that helps us understand the chance that a certain event can happen out of all the possible events. In other words, probability quantifies the likelihood or belief that an event will occur.

For example, it might or might not rain on a given day. Hence, there are two possible events – rain and no rain – and each of these two events has a certain probability associated with it. Similarly, when you toss a coin, the two possible events are heads and tails, and each of these two outcomes has a certain probability associated with it.

As per the classical approach, you were introduced to a simple formula for calculating the probability of an event when all the possible events are equally likely to occur. This formula is given as follows:

$P r o b a b i l i t y o f a n e v e n t = \frac{N u m b e r o f f a v o u r a b l e e v e n t s}{T o t a l n u m b e r o f e q u a l l y l i k e l y e v e n t s}$

It is important to remember that the given formula is applicable only when all the possible events are equally likely.

Going ahead, Thomas will introduce you to calculating probabilities when multiple events can occur and after that, he will also introduce you to two other approaches of calculating probability.

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In the video above, you learnt that the calculation for probability, in the case of multiple events occurring, typically follows the below rules: (P stands for probability)

1. The value of the probability of any event always lies between 0 and 1. This is fairly intuitive as on the extreme ends, the event is either impossible (for instance, the probability of rolling a regular die and getting a ‘7’ on the face) or it always occurs (for instance, the probability of tossing a regular coin and getting either heads or tails). Most events, however, lie somewhere in between. The mathematical representation of the range that the probability of an event A can take is as follows:

0 ≤ P(A) ≤ 1

2. According to the addition rule of probability, if two events, A and B, are mutually exclusive (both events cannot occur at the same time) then the probability that either of them occurs is equal to the sum of their individual probabilities. The mathematical representation of this is as follows:

P(A 'or' B) = P(A) + P(B); if A and B are mutually exclusive events

The outcomes of tossing a coin or rolling a die are mutually exclusive. In other words, you cannot get both ‘3’ and ‘5’ on rolling a regular die once. Hence, the probability of getting either '3' or '5' is equal to the sum of the probability of getting '3' and that of getting '5'.

3. According to the multiplication rule of probability, if two events, A and B, are independent (the occurrence of one event does not affect the probability of occurrence of the other) then the probability that both of them occur is equal to the multiplication of their individual probabilities. The mathematical representation of this is as follows:

P(A 'and' B) = P(A) * P(B); if A and B are independent events

The outcomes of tossing a coin or rolling a die multiple times are independent of each other. In other words, no matter what you get on the first toss, the probability of getting either a heads or tails remains unchanged for the second toss.

To consolidate your understanding of the above rules, you can follow the example presented in the document below.

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After the example, you learnt about the empirical and subjective approaches to calculating probability.

The empirical/frequentist approach, where probabilities are derived from observations. Hence, if you want to find the probability of getting heads on tossing a coin, you will toss the coin several times and note down the outcome of each trial.

Let’s say you tossed the coin 10,000 times and got heads 5,052 times and tails 4,948 times. Following the frequentist approach, you would conclude that the probability of getting heads is 0.5052 and that of getting tails is 0.4948 for that particular coin.

Another way of arriving at the probability of an event is the subjective approach, which reflects an individual’s understanding and judgement of how likely the outcomes are.

In the next segment, you will learn how to calculate probability in Excel.