Assignment 2

# Assignment 2 - SMSL/07 THE UNIVERSITY OF HONG KONG...

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SMSL/07 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Assignment 2 Section A 1. Let A,B,C be events such that A B C = Ω (complete sample space) and P ( A ) = 0 . 55 , P ( B ) = 0 . 65 , P ( C ) = 0 . 4 , P ( A B ) = 0 . 3 , P ( B C ) = 0 . 2 , P ( C A ) = 0 . 2 . (a) Calculate P ( A B ), P ( B C ) and P ( C A ). (b) Calculate P ( A B C ) and P ( A B C ). (c) Calculate P ( A \ B ) and P ( B \ A ). (d) Calculate P ( A | B ) and P ( B | A ). (e) Calculate P ( C | A \ B ) and P ( C | B \ A ). 2. Two drugs, A and B, are known to cure diabetes with certain degrees of success. The recovery probabilities of diabetics treated with the two drugs are given respectively as follows. Men Women Drug A 0.20 0.85 Drug B 0.15 0.80 A medical experiment is carried out to verify the above ﬁgures. The dealer of drug A has suggested treating 80 men and 20 women patients with drug A in the experiment. A quota of

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Assignment 2 - SMSL/07 THE UNIVERSITY OF HONG KONG...

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