1 Suppose P A 0 45 P A B 0 15 P B 0 40 P A C 0 20 P C 0 50 P B C 0 25 P A B C 0 05 a Find P A B C b Find P A B C c Find P A B C 2 Find the value of a Suppose S 0 2 4 6 8 even non negative integers and p that would make this a valid probability model P 0 p b P k 1 3k k 2 4 6 8 Suppose S 1 2 3 4 positive integers and P 1 p P k ln 3 k k C 5k k 2 3 4 3 Suppose S 3 4 5 6 and P k a Find the value of C that would make this a valid probability model b Find P even outcome k 3 4 5 6 4 At Initech 60 of all employees surf the Internet during work hours 24 of the employees surf the Internet and play MMORPG during work hours It is also known that 72 of the employees either surf the Internet or play MMORPG or both during work hours a What proportion of the employees play MMORPG during work hours b If it is known that an employee surfs the Internet during work hours what is the probability that he she also plays MMORPG c Suppose an employee does not play MMORPG during work hours What is the probability that he she surfs the Internet 1 P A 0 45 Suppose P A B 0 15 P B 0 40 P A C 0 20 P C 0 50 P B C 0 25 P A B C 0 05 a Find P A B C P A B C 0 80 OR P A B C P A P B P C P A B P A C P B C P A B C 0 45 0 40 0 50 0 15 0 20 0 25 0 05 0 80 b Find P A B C P A B C 0 65 OR P A B C P A P B C P A B C 0 45 0 25 0 05 0 65 c Find P A B C P A B C 0 30 p 2 Find the value of a Suppose S 0 2 4 6 8 even non negative integers and that would make this a valid probability model P 0 p P k 1 k 3 k 2 4 6 8 1 p 0 p 2 p 4 p 6 p 8 p 1 32 1 34 1 36 1 38 p 1 9 1 1 9 p 1 8 p 7 8 b Suppose S 1 2 3 4 positive integers and P 1 p P k ln 3 k k k 2 3 4 p x 1 Must have p 1 all x k 2 k 2 ln 3 k k ln 3 k ln 3 k k k 0 k 1 1 ln 3 e ln 3 1 ln 3 2 ln 3 p 1 2 ln 3 1 p 1 ln 3 1 0 0986 C k 5 3 Suppose S 3 4 5 6 and P k a Find the value of C that would make this a valid probability model C C 3 first term k 1 base 5 1 k 3 5 1 5 b C 125 4 5 k 3 4 5 6 C 1 100 C 100 Find P even outcome P even outcome p 4 p 6 p 8 100 100 5 4 100 5 6 100 5 8 first term 1 base 54 1 1 52 4 24 1 6 4 At Initech 60 of all employees surf the Internet during work hours 24 of the employees surf the Internet and play MMORPG during work hours It is also known that 72 of the employees either surf the Internet or play MMORPG or both during work hours P Internet MMORPG 0 24 P Internet 0 60 P Internet MMORPG 0 72 a What proportion of the employees play MMORPG during work hours P Internet MMORPG P Internet P MMORPG P Internet MMORPG 0 72 0 60 P MMORPG 0 24 P MMORPG 0 36 b MMORPG MMORPG Internet 0 24 0 36 0 60 Internet 0 12 0 28 0 40 0 36 0 64 1 00 If it is known that an employee surfs the Internet during work hours what is the probability that he she also plays MMORPG P MMORPG Internet c P MMORPG Internet 0 24 0 40 P Internet 0 60 Suppose an employee does not play MMORPG during work hours What is the probability that he she surfs the Internet P Internet MMORPG P Internet MMORPG 0 36 9 0 5625 0 64 16 P MMORPG
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