Hey Developer’s, I’m back with a new topic which is Conditional and Unconditional Probability in the series of statistics foundations.

Quick Refresher

Probability of Union Of Events – Statistics Part 15

So, let’s get started …

Let’s Understand With Example, First

Unconditional Probalility : Probability that it will rain today giving no additional information.

Conditional Probability : Probability that it will rain today given it’s been raining an enitre week.

Here you can see that the unconditional probaility does not depends on other obervations, but the conditional probability depends on the other observations. There are some previous factors which need to take care while working on conditional probability because it depends on that factors.

Conditional Probability

Conditional probability is defined as the likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.

{\displaystyle P(A\mid B)={\frac {P(A\cap B)}{P(B)}},}

assuming P(B) > 0 .The formula states that the probability of “A given B” and written as P(A|B), where the probability of A depends on that of B happening.

P(A|B) is derived by multiplying the probability of both A and B occurring and dividing that product by the probability of A by itself.


In a group of 100 sports car buyers, 40 bought alarm systems, 30 purchased bucket seats, and 20 purchased an alarm system and bucket seats. If a car buyer chosen at random bought an alarm system, what is the probability they also bought bucket seats?

Step 1: Figure out P(A). It’s given in the question as 40%, or 0.4.

Step 2: Figure out P(A∩B). This is the intersection of A and B: both happening together. It’s given in the question 20 out of 100 buyers, or 0.2.

Step 3: Insert your answers into the formula:
P(B|A) = P(A∩B) / P(A) = 0.2 / 0.4 = 0.5.

The probability that a buyer bought bucket seats, given that they purchased an alarm system, is 50%.

Venn diagram showing that 20 out of 40 alarm buyers purchased bucket seats.

Unconditional Probability

Unconditional Probability is defined as the likelihood that an event will take place independent of whether any other events take place or any other conditions are present.

The unconditional probability of an event can be determined by adding up the outcomes of the event and dividing by the total number of possible outcomes.

For example, if a die lands on the number five 15 times out of 60, the unconditional probability of landing on the number five is 25% (15 outcomes /60 total lots = 0.25).

There is one example from one of the blog ,

As a hypothetical example from finance, let’s examine a group of stocks and their returns. A stock can either be a winner, which earns a positive return, or a loser, which has a negative return. Say that out of five stocks, stocks A and B are winners, while stocks C, D, and E are losers. What, then, is the unconditional probability of choosing a winning stock? Since two outcomes out of a possible five will produce a winner, the unconditional probability is 2 successes divided by 5 total outcomes (2 / 5 = 0.4), or 40%.

Next Post will be on Independence of Events

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