1. CIVL 181 Tutorial 2 Total probability Bayes theorem

2. s.i. and m.e.: Contractors A and B bidding for jobs (1)bidding for different jobs (2) bidding for same job AB AB

3. E 1 and E 2 are s.i. Should E 1 and E 2 partly overlap in Venn? Yes! Because occurrence of E 1 should not prohibit E 2 (and vice versa) P (E 2 | E 1 ) 0 = P(E 2 ) s.i. and m.e.: Contractors A and B bidding for jobs

4. Ture or false?

5. Example Three bags of apples. Bag 1 has 10% bad apples, Bag 2 has 20% bad apples, bag 3 has 40% bad apples. i)Suppose you select one of three (at random), and pick an apple from the selected bag. The apple turned bad, what is the chance that it is from Bag 1, Bag 2, Bag3 ?(1/7,2/7,4/7) ii)Suppose an apple picked is good, what is the chance from Bag 1, Bag 2, Bag 3 ?(9/23,8/23,6/23)

6. Example