m1f11sol

# m1f11sol - D | - | D | - | CTD c | = 5 . Finally | C c D c...

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Midterm 1 solutions. (1) (a) To describe a seating arrangement we need to (I) To choose the driver (2 ways) (II) To choose the front passanger (2 ways) (III) Sit remainig people (3!=6 ways) Therefore there are 2 × 2 × 6 = 24 possibilities. (b) At step 2 we have two possibilities only one of which is good (Cecilia does not sit in front) so the answer is 1 2 . (2) (a) There are ± 11 2 , 2 , 2 , 1 , 1 , 1 , 1 ² = 11! 2 3 possibilities. (b) We need to (I) Choose the ﬁrst(=last) letter (3 ways) (II) Arrange 9 remaining letters ( ± 9 2 , 2 , 1 , 1 , 1 , 1 ² = 9! 2 2 ) ways so the answer is 3 × 9! 2 2 . (3) (a) Let C,D,T denote the event that the senator accepts illegal contributions (respectivelt uses drags, cheats on taxes). Then | CDT c | = | CD |-| CDT | = 10 , | CTD c | = | CT |-| CDT | = 5 , | DTC c | = | DT |-| CDT | = 1 . Next | TC c D c | = | T | - | TCD c | - | TCC c | - | CDT | = 10 , | DT c C c | = | D T | - | T | - | DCT c | = 20 . Thus | CD c T c | = | C

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Unformatted text preview: D | - | D | - | CTD c | = 5 . Finally | C c D c T c | = | S | - | T | - | CDT c | - | CD c T c | - | DC c T c | = 9 . (b) Due to part (a) the answer is ± 9 2 ² ± 100 2 ² = 9 × 8 100 × 99 . (4) (a) We have 12 balls 9 of which are non green. If 2 green balls are chosen then 4 non green balls are chosen. Therefore the answer is ± 3 2 ²± 9 4 ² ± 12 6 ² . (b) Let R,B,G and W denote the event that red (respectively blue, green or white) is complete. Similarly to part (a) we have P ( R ) = ± 9 3 ² ± 12 6 ² , P ( RB ) = 1 ± 12 6 ² , P ( RBG ) = 0 1 2 and similar formulas for other colors. Thus the answer is ± 4 1 ² ± 9 3 ² ± 12 6 ²-± 4 2 ² 1 ± 12 6 ² ....
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## This note was uploaded on 02/09/2012 for the course STAT 410 taught by Professor Staff during the Spring '08 term at Maryland.

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m1f11sol - D | - | D | - | CTD c | = 5 . Finally | C c D c...

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