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
union sets probability

probability with union sets

We have:
A ? B = (X ? A) ? (A ? B) ? (Y ? B)   (1)
Then:
P(A ? B) = P(X ? A) + P(A ? B) + P(Y ? B)   (1')

A = (X ? A) ? (A ? B)   (2)
B = (Y ? B) ? (A ? B)   (3)

P(A) = P(X ? A) + P(A ? B)   (2')
P(B) = P(Y ? B) + P(A ? B)   (3')

P(X ? A) = P(A) - P(A ? B)    (2")
P(Y ? B) = P(B) - P(A ? B)   (3")

P(A ? B) = P(X ? A) + P(A ? B) + P(Y ? B) (1")
= P(A) - P(A ? B) + P(A ? B) + P(B) - P(A ? B)
= P(A) + P(B) - P(A ? B)

P(A ? B) = P(A) + P(B) - P(A ? B)

P(A ? B) = P(A) + P(B) - P(A ? B)

 Today: : ____________

calculator for combinatorics probability and Statistics