More Hard Problems Using Bayes' Theorem, Please

From: Lee Corbin (lcorbin@tsoft.com)
Date: Sat Jul 05 2003 - 23:06:16 MDT

  • Next message: Lee Corbin: "RE: Cutting Taxes to Spur the Economy"

    Has anyone got more hard problems using Bayes' Theorem?
    The ones in my textbooks aren't that challenging, e.g.,
    #2 below. It was here on this list that the following
    great problems were posted.

    Any more?

    Thanks,
    Lee

    1. It is known that about 1 woman in 100 gets breast cancer.
       When a woman does have breast cancer, the test detects it
       80 percent of the time. About one time in ten, however,
       the test creates a false-positive; that is, someone who
       does not have breast cancer nonetheless gets a positive
       reading from the test. Given that a particular woman has
       just scored positive on the test, what is the actual
       probability that she has breast cancer?

    2. If there is a burglary on a particular night the probability
       is .99 that the burglar alarm will ring. If there is no
       burglary on a particular night the probability is .005 that
       the burglar alarm will ring, falsely. The probability is
       .001 that a burglary will occur on a particular night.
       What is the probability that there is a burglary, given
       that the alarm just rang?

    3. The probability that a newborn will have deformities
       traceable to a sickness of its mother during pregnancy is 1%.
       If a child is born healthy and normal, the probability that
       the mother had rubella during her pregnancy is 10%. If a
       child is born with deformities and it can be traced to some
       sickness of the mother, the probability that the mother had
       rubella during her pregnancy is 50%. What is the probability
       that a child will be born with deformities if its mother had
       rubella during her pregnancy?

    4. (and Eliezer's egg problem, which I don't have ready to hand).

    5. A nurse has just started to count the babies in a hospital
       nursery. She has just counted that there are two boys, and has
       not counted the girls, when, at 11:00, a new baby is brought
       in to the nursery. A baby is then selected at random, from
       all the babies present, to have its footprint taken. The
       selected baby happens to be a boy. What is the probability
       that the baby added at 11:00 was a girl?

    This archive was generated by hypermail 2.1.5 : Sat Jul 05 2003 - 23:15:18 MDT