In 5166, determine whether each infinite geometric series converges or diverges. If it converges, find its sum.

Independent and Dependent Events Two events A and B are independent neither event affects the other Example: tossing a coin and a 6-sided die A= the coin gives a head B= the die gives a three A and B is independent, what is the probability of getting a head and a three P(A and B) S= {H1 H2 H3 H4 H5 H6 T1 T2 T3 T4 T5 T6} P(A)= 6/2= ½ P(B)= 2/12= 1/6, P(A)*P(B)= ½ * 1/6= 1/12 In general, if A and B are independent P (A and B) = P(A) * P(B) If you have two event that are not independent, it is dependent, and one will affect the other. Example: a bag contains 3 red marbles and 2 green marbles. A marble is drawn from the bag. Recorded and put back in the bag and then another one is drawn. What is the probability of both are red both time A= first time being red B= second time be