Examples of Joint Probability

Example 1: Independent Events

Suppose you are running an e-commerce platform, and you want to find the probability of a customer purchasing a red shirt (event A) and a blue hat (event B) independently. Find out the Joint Probability where

P(A): The probability of a customer buying a red shirt is 0.3.

P(B): The probability of a customer purchasing a blue hat is 0.2.

Solution:

P(A∩B) = P(A) x P(B)

P(A∩B) = P(customer buying a red shirt) x P(customer buying a blue hat)

P(A∩B) = 0.3 x 0.2

P(A∩B) = 0.6

Example 2: Dependent Events

Imagine you are in the insurance business, and you want to determine the probability of a customer filing a claim (event A) and receiving a payout (event B), given that a claim was filed. Find out the Joint Probability where

P(A): The probability of a customer filing a claim is 0.1.

The probability of a customer receiving a payout given that a claim was filed is 0.8.

Solution:

P(A∩B) = P(A) x P(B|A)

P(A∩B) = P(customer filing a claim) x P(customer receiving a payout given that a claim was filed)

P(A∩B) = 0.1 x 0.8

P(A∩B) = 0.08

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.