# Let’s start this blog by a fun fact about probability:

“In a room of just 23 people there is a 50% chance of any two sharing a birthday. In a room of 75 people this becomes 99.9%.”

Amazing isn’t it?

Now let’s move on to our next section in which I’ll tell you some amazing concepts related to Bayesian Statistics in layman terms so that every one can understand it on their own.

To Chaliye shuru krte hai 😉

**Introduction :**

We will cover the concept of conditional probabilities in this blog and we’ll how can a conditional probability change out perspective of the statistics world.

In words, conditional probability is written as:

“Probability of an event A given B equals the probability of B and A happening together divided by the probability of B”.

Whereas in terms of formula it is written as:

I am sure you are a bit confused as of now. But don’t worry by the end of this blog you’ll get everything.

Let’s understand P (A and B) probability using vein diagram:

The Green circle defines the P(A) and the Blue one defines P(B) and the interaction part is P (A and B).

The formula for calculating the intersection part is:

P (A and B) = P(A) + P(B) – P(A U B)

**Example:**

In a group of 100 bulbs, 40 have blue light, 30 have green light and 20 have bit (switchable).

If a buyer chosen at random bought Blue one, what is the probability they also bought green ones?

**Soln: **

Step1: Figure out P(A). It is given in the question as 0.4

Step2: Figure out the intersection of both A and B: both happening together. It is also give in the question as 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 Green light, given that they purchased blue one, is 50%.

**Conditional Probability in Real Life:**

Conditional probability is used in many areas, in fields as diverse as calculus, insurance, and politics. For example, the re-election of a president depends upon the voting preference of voters and perhaps the success of television advertising—even the probability of the opponent making gaffes during debates!

The weatherman might state that your area has a probability of rain of 40 percent. However, this fact is conditional on many things, such as the probability of…

…a cold front coming to your area.

…rain clouds forming.

…another front pushing the rain clouds away.

We say that the conditional probability of rain occurring depends on all the above events.

**Wrapping up**

I hope you know understands what is a conditional probability and how it is used in the real life. In the next lesson we’ll learn from where the conditional probability formula came and derive the Bayes theorem as well.

Now let’s test your understanding:

Written by Vivek Mittal ( Graduate in B.com (hons) from University of Delhi and 2 Actuarial Papers passed from IFOA )