Conditional Probability with Example || Lesson 32 || Probability & Statistics || Learning Monkey ||

Conditional Probability with Example
In this class, We discuss Conditional Probability with Example.
The reader should have prior knowledge of dependent events. Click Here.
Conditional Probability
P(A|B) = P(A ∩ B) / P(B)
P(A|B) = probability of event A given event B happened.
We understand the conditional probability equation with an example.
Example:
Random Experiment: Toss two dice.
Event A = the sum of the values on the two dice is seven.
Sample space S = 36
A = {(5,2), (2,5), (3,4), (4,3), (6,1),(1,6}
P(A) = 6/36
If there is no condition our sample space S = 36.
We are using the full sample space.
Conditional probability P(A|B)
Event B = obtained five on one of the dice.
Event A = sum of the values on the dice = 7
It was given event B happened whenever event B happened sample space changes.
The new sample space S1 = {(1,5), (5,1), (2,5), (5,2), (3,5), (5,3), (5,4), (4,5), (5,5), (6,5), (5,6)}
S1 = 11
the happening event A called conditional probability in the new sample space.
There are two chances in the new sample space {(2,5), (5,2)}
P(A|B) = 2/11
Now we relate the conditional probability value 2/11 with our equation.
P(A|B) = P(A ∩ B) / P(B)
P(A ∩ B) = 2/36
P(B) = 11/36
If we cancel 36 from the numerator and denominator, we get 2/11

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[muralisub]

Bro... you teaching with examples are good for people interested in data science fundamentals.

[maryamyuusufi]

thank you so much for good explanation and that you make it easy to understand