math 105 Prelim2 +key 2004 - Math 105, Fall 2004 Solutions...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 105, Fall 2004 Solutions to Prelim 2 1. (a) Henri has to take 3 bottles from 5+7=12, and the order in which they are taken doesnt matter. Therefore, there are 12 3 = 12! 9! 3! = 12 11 10 9! 9! 3! = 12 11 10 3! = 1320 6 = 220 possible choices. (b) Henri has to choose 1 bottle from the 5 bottles of red and 2 bottles from the 7 bottles of white. By the multiplication principle, there are 5 1 7 2 = 5 21 = 105 ways of doing this. 2. Note that S = { , 1 , 2 , . . . , 98 , 99 } is the sample space for this problem. (a) E = { , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 } . F = { 9 , 18 , 27 , 36 , 45 , 54 , 63 , 72 , 81 , 90 } . Assuming equally likely outcomes, we have: P ( E ) = n ( E ) n ( S ) = 20 100 = 1 5 and P ( F ) = n ( F ) n ( S ) = 10 100 = 1 10 . (b) Assuming equally likely outcomes, P ( E F ) = n ( E F ) n ( s ) = n ( { 9 , 18 } ) 100 = 2 100 = 1 50 . So by definition of conditional probability, we have: P ( E | F ) = P ( E F ) P ( F ) = 1 / 50 1 / 10 = 1 5 . Hence P ( E ) = 1 5 = P ( E | F ), and so E and F are independent events. (c) G = { 5 , 14 , 23 , 32 , 41 , 50 } . So assuming equally likely outcomes, we have P ( G ) = n ( G ) n ( S ) = 6 100 = 3 50 and P ( E G ) = n ( E G ) n ( S ) = n ( { 5 , 14 } ) 100 = 2 100 = 1...
View Full Document

This note was uploaded on 04/21/2008 for the course MATH 1105 taught by Professor Hurtado during the Fall '07 term at Cornell University (Engineering School).

Page1 / 5

math 105 Prelim2 +key 2004 - Math 105, Fall 2004 Solutions...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online