Formula for Joint Probability

The formula for calculating joint probability hinges on whether the events are independent or dependent:

1. For Independent Events

When events A and B are independent, meaning that the occurrence of one event does not impact the other, we use the multiplication rule:

P(A∩B) = P(A) x P(B)

Here, P(A) is the probability of occurrence of event A, P(B) is the probability of occurrence of event B, and P(A∩B) is the joint probability of events A and B.

2. For Dependent Events

Events are often dependent on each other, meaning that one event’s occurrence influences the likelihood of the other. Here, we employ a modified formula:

P(A∩B) = P(A) x P(B|A)

Here, P(A) is the probability of occurrence of event A, P(B|A) is the conditional probability of occurrence of event B when event A has already occurred, and P(A∩B) is the joint probability of events A and B.

Probability theory is a cornerstone of statistics, offering a powerful tool for navigating uncertainty and randomness in various fields, including business. One key concept within probability theory is Joint Probability, which enables us to analyse the likelihood of multiple events occurring simultaneously.