1. CSE 221: Probabilistic Analysis of Computer Systems Topics covered: Combinatorial problems Conditional probability Independent events (Sec. 1.8.2-1.8.3,1.9-1.10)

2. Combinatorial problems  Ordered sample of size k without replacement

3. Combinatorial problems (contd..)  Example: Ordered sample of size k without replacement

4. Combinatorial problems (contd..)  Example: Ordered sample of size k without replacement

5. Combinatorial problems (contd..)  Unordered sample of size k, without replacement

6. Combinatorial problems (contd..)  Example: Unordered sample of size k, without replacement

7. Combinatorial problems (contd..)  Example: Unordered sample of size k, without replacement

8. Conditional probability  Assigning probabilities to events:  How does the probability of an event change, given that some information is available about another event.

9. Conditional probability (contd..)  Example:

10. Independent events  Definition:  Mutually independent events:  Pairwise independent events:

11. Independent events (contd..)  Example:

12. Reliability of a series system  Description of a series system:  Reliability of a component:  Reliability of a series system:

13. Reliability of a series system (contd..)  Example: