hw09sol - Math 55: Discrete Mathematics, Fall 2008 Homework...

Info iconThis preview shows page 1. Sign up to view the full content.

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

Unformatted text preview: Math 55: Discrete Mathematics, Fall 2008 Homework 9 Solutions * 6.3: 4. Let F be the event that Ann selects an orange ball, E the event that she chooses box 2. Then p ( E ) = 1 / 2, p ( F | E ) = 5 / 11, p ( F | E ) = 3 / 7. Bayes Theorem gives p ( E | F ) = (5 / 11)(1 / 2) / ((5 / 11)(1 / 2) + (3 / 7)(1 / 2)) = 35 / 68. 10. (a) ( . 97)( . 04) / (( . 97)( . 04) + ( . 02)( . 96)) . 669 (b) ( . 02)( . 96) / (( . 97)( . 04) + ( . 02)( . 96)) . 331 (c) ( . 03)( . 04) / (( . 03)( . 04) + ( . 98)( . 96)) . 00127 (d) ( . 98)( . 96) / (( . 03)( . 04) + ( . 98)( . 96)) . 9987 12. (a) ( . 9)(2 / 3) + ( . 2)(1 / 3) = 2 / 3 (b) p (send 0 | receive 0) = p (receive 0 | send 0) p (send 0) /p (receive 0) = . 9(2 / 3) / (2 / 3) = . 9 14. (3 / 8)(1 / 2) / ((2 / 7)(1 / 6) + (3 / 8)(1 / 2) + (1 / 2)(1 / 3)) = 7 / 15 6.4: 4. 10( . 6) = 6 8. 3(7 / 2) = 21 / 2 16. p ( X = 0) = 1 / 4, p ( Y = 0) = 1 / 4, but p ( X = 0 | Y = 0) = 0 6 = (1 / 4)(1 / 4). You could also use other values of these random variables to give a counterexample to independence.also use other values of these random variables to give a counterexample to independence....
View Full Document

Ask a homework question - tutors are online