Question

1) Show that for every 1 Sisn, P(AA)>o 2) Show that PA, n nA")-P(AJPA,İA, )PA,İA, n As) P(A"IA, n nA"-.). Remark. This identity is called the compound probability theorem and is for instance useful in situations where the pašt has an influence on the future (and is in some sense the probabilistic version of the "multiplicative rule") 3) (Application) Consider an urn with 6 identical blue balls and 4 identical red balls. Take one after the other 3 balls at random. What is the probability that the 3 balls are red? Hint. You may introduce the event A: "the i-the bal is red'"

Answer 1

Compound probability theorem:-