{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Ch. 6 Bayes' Rule - 1 Inductive Logic PHIL 111 Fall 2009...

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

View Full Document Right Arrow Icon
1 Inductive Logic PHIL 111 Fall 2009 Chapter 7 Bayes’ Rule Bayes’ Rule: Pr(H/E) = Pr(H j ) Pr(E/H j )]) / ∑ [Pr(H i) Pr(E/H i )] = Pr(H)Pr(E/H) / Pr(H)Pr(E/H) + Pr( H)Pr(E/ H) 1 . A tarantula is a large, fierce-looking, and somewhat poisonous tropical spider. Once upon a time, 3% of consignments of bananas from Honduras were found to have tarantulas on them, and 6% of the consignments from Guatemala had tarantulas. 40% of the consignments came from Honduras and 60% came from Guatemala. Let G = The lot came from Guatemala. Let H = The lot came from Honduras. Let T = The lot had a tarantula on it. a. A tarantula was found on a randomly selected lot of bananas. What is the probability that this lot came from Guatemala? b. What is the probability that this lot came from Honduras, given that a tarantula was discovered in a randomly selected lot of bananas? c. What is the probability that a lot had tarantulas in it, given that it came from Honduras? 2 . [Base rates] Odd Question 5 You have been called to jury duty in a town where there are two taxi companies, Green Cabs Ltd. and Blue Taxi Inc. Blue Taxi uses cars painted blue. Green Cabs uses green cars. Green Cabs dominate the market, with 85% of the taxis on the road. On a misty winter night, a taxi side swiped another car and drove off. A witness says it was blue cab. The witness is tested under conditions like those on the night of the accident, and 80% of the time she correctly reports the color of the cab that is seen. That is, regardless of whether she is shown a blue or a green cab in misty evening light she gets the color right 80% of the time. Let G = A taxi selected at random is green. Let B = A taxi selected at random is blue. Let W b = A witness claims that the taxi is blue. a. The witness says it was a blue cab. What is the probability that it was a blue cab? b. Mark the branch of the probability tree with a (1) indicating the true positive result, with a (2) indicating the false positive result, with a (3) indicating the true negative result, and with a (4) highlighting the false negative result of the test. 3 . Consider a pregnancy test that claims to detect 99% of all pregnancies it is used on; it will produce a false positive report 5% of the time. a. Suppose that to begin with there is a 99% chance that a woman is not pregnant – because she has been using a method of birth control which claims to be 99% effective. Suppose she uses this pregnancy test and it says that she is pregnant, i.e. the test says “yes” (Y). What is the probability that she is pregnant given this result?
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
Image of page 2
This is the end of the preview. Sign up to access the rest of the 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