Contents
 • one choice • many choices: permutations • many choices: combinations • many choices: combinations • independent events • dependent events • permutations without repettitions • permutations with identical elements • combinations • coditional probabilities • and or events • two outcomes • total probability theorem • Bayes rule • union sets and probability • fundamental counting principle

 Other exercices

 Combinatorics - Probability
Conditional probability

Conditional probability

Let's consider the following set of books from which a winner can get 2 books:
Books = {Physics1, Physics2, Physics3, Math1, Math2, History, philosophy}

Let's write:
A is the event associated to "win a Physics book", and B is the event associated to "win a Math book"

The probability to win, at first, a Physics book, is: P(A) = 3/7

The probability to win a Physics book and then a Math book is: P(A ∩ B ) = 3/7 x 2/6 = 1/7

What is the probability to win a Math book given that it have been, at first, won a Physics book ?

P(B/A) = p(B ∩ A)/p(A) = (1/7) / (3/7) = 1/3 = 33%

The conditional probability of an event B linked to an event A is the probability that event B occurs given that the event A has already occurred.

The probability of B given A is :

P(B/A) = P(B ∩ A)/ P(A)

 Today: : ____________

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