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## CIVL 181 Tutorial 2

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**CIVL 181 Tutorial 2**• Total probability • Bayes theorem**s.i. and m.e.:Contractors A and B bidding for jobs**(1) bidding for different jobs (2) bidding for same job A B A B**s.i. and m.e.:Contractors A and B bidding for jobs**• E1 and E2 are s.i. • Should E1 and E2 partly overlap in Venn? • Yes! Because occurrence of E1 should not prohibit E2 (and vice versa) P (E2 | E1) 0 = P(E2)**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)