{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

sec_2_4_part2_sol - (0 40(0 70(0 40(0 70(0 90(0 30 ≈...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
APPM 4/5570 Solutions to Problems from Section 2.5 55. Let L be the event that a randomly selected tick carries Lyme disease and let H be the event that a randomly selected tick carries HGE. We are given that P ( L ) = 0 . 16 , P ( H ) = 0 . 10 , and P ( L H | L H ) = 0 . 10 . We want to find P ( L | H ) = P ( L H ) P ( H ) . Note that 0 . 10 = P ( L H | L H ) = P (( L H ) ( L H )) P ( L H ) = P ( L H ) P ( L H ) which implies that P ( L H ) = 0 . 10 · P ( L H ) = 0 . 10 · [ P ( L ) + P ( H ) - P ( L H )] . So, P ( L H ) = 0 . 10 P ( L ) + 0 . 10 P ( H ) - 0 . 10 P ( L H ) which implies that 1 . 10 P ( L H ) = 0 . 10 P ( L ) + 0 . 10 P ( H ) = (0 . 10)(0 . 16) + (0 . 10)(0 . 10) . So, P ( L H ) = (0 . 10)(0 . 16) + (0 . 10)(0 . 10) 1 . 10 0 . 02363636 . The final answer is then P ( L | H ) = P ( L H ) P ( H ) 0 . 02363636 0 . 10 0 . 2364 . 60. Let L be the event that an aircraft has a locator and let D be the event that an aircraft is discovered. We are given that P ( D ) = 0 . 70 , P ( L | D ) = 0 . 60 , P ( L 0 | D 0 ) = 0 . 90 Note then that we also now know that P ( D 0 ) = 0 . 30 , P ( L 0 | D ) = 0 . 40 , P ( L | D 0 ) = 0 . 10 Using Bayes Rule, we get:
Image of page 1

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

View Full Document Right Arrow Icon
a. P ( D 0 | L ) = P ( L | D 0 ) · P ( D 0 ) P ( L | D ) · P ( D ) + P ( L | D 0 ) · P ( D 0 ) = (0 . 10)(0 . 30) (0 . 60)(0 . 70) + (0 . 10)(0 . 30) 0 . 06667 b. P ( D | L 0 ) = P ( L 0 | D ) · P ( D ) P ( L 0 | D ) · P ( D ) + P ( L 0 | D 0 ) · P ( D
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (0 . 40)(0 . 70) (0 . 40)(0 . 70) + (0 . 90)(0 . 30) ≈ . 50901 62. Let B be the event that the purchasher has a basic model, let D be the event that the purchaser has a deluxe model. Let E be the event that the purchaser has an extended warranty. We are given that P ( B ) = 0 . 40 (and hence we know that P ( D ) = 0 . 60) and we are given that P ( E | B ) = 0 . 30 , P ( E | D ) = 0 . 50 . So, we know that P ( E | B ) = 0 . 70 , P ( E | D ) = 0 . 50 . The answer, by Bayes Rule, is then P ( B | E ) = P ( E | B ) · P ( B ) P ( E | B ) · P ( B ) + P ( E | D ) · P ( D ) = (0 . 30)(0 . 40) (0 . 30)(0 . 40) + (0 . 50)(0 . 60) ≈ . 2857...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern