1. A stockbroker knows from the past experience that the probability that a client owns stocks is 0.7 and the probability that a client owns bonds is 0.4. The probability that the client owns bonds if he/she already owns stock is 0.35. (1) What is the probability that the client owns both of these securities? (2) Given that the client own bonds, what is the probability that the client owns stocks?

2. Suppose that E is an event such that Pr(E)=0 and that F is any other event, Are E and F independent events?

(Hint: Pr(A|B) = Pr(A∩B)/Pr (B))

3. Suppose that for a given year there is a 2% chance that your desktop computer will crash and a 5% chance that your laptop computer will crash. And there is a 0.1 % chance that both computers will crash. Is the reliability of the two computers independent of each other?

4. Amy walks to work and sometimes she bicycles when the weather is nice. In bad weather she takes the metro or she car pools with friends. Based on the past habits there is 35% probability that Amy walks, 30% she uses her bike, 20% car pools, and 15% he takes the metro.

If Amy walks, there is a 5% probability of being late to the office; if she cycles there is a 10% chance of being late; a 45% chance of being late if he car pools because of traffic; and a 20% chance of being late if she takes the metro.

(1) On any given day, what is the probability of Amy being late to work?

(2) On any given day, what is the probability of Amy being on time to work?

(3) Given that Amy is late one day, what is the probability that she used the bicycle?

(4) Given that Amy takes the metro one day, what is the probability that he will arrive on