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 Link for playlists:    / @wisdomerscse   Link for our website: https://learningmonkey.in Follow us on Facebook @   / learningmonkey   Follow us on Instagram @   / learningmonkey1   Follow us on Twitter @   / _learningmonkey   Mail us @ [email protected]