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Probability question: Ms. Aquina has just had a biopsy

  1. Apr 19, 2012 #1
    Probability question: "Ms. Aquina has just had a biopsy ..."

    1. The problem statement, all variables and given/known data

    Ms. Aquina has just had a biopsy on a possibly cancerous tumor. Not wanting to spoil a weekend family even, she does not want to hear any bad news in the next few days. But if she tells the doctor to call only if the news if good, then if the doctor does not call, Ms. Aquina can conclude that the news is bad. So, being a student of probability, Ms. Aquina instructs the doctor to flip a coin. If it comes up heads, the doctor is to call if the news is good and not call if the news is bad. If the coin comes up tails, the doctor is not to call. in this way, even if the doctor doesn't call, the news is not necessarily bad. Let A be the probability that the tumor is cancerous; let B be the conditional probability that the tumor is cancerous given that the doctor does not call. Prove the B > A.

    2. Relevant equations

    Baye's forumla

    3. The attempt at a solution

    This has me confused. I'll explain my though process and then you can correct me and perhaps help me prove this for me.

    B = P(Tumor is cancerous | Doc doesn't call) = P(Tumor is cancerous & Doc doesn't call) / P(Doc doesn't call) = P(Doc doesn't call | Tumor is cancerous) * P(Tumor is cancerous) / P(Doc doesn't call) = 1 * A / P(Doc doesn't call) = ??????

    I can't figure out the probability that the Doc doesn't call.
     
  2. jcsd
  3. Apr 19, 2012 #2

    HallsofIvy

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    Re: Probability question: "Ms. Aquina has just had a biopsy ..."

    If A is the probability the tumor is cancerous, then 1- A is the probability it is not.

    If the tumor is cancerous, the Dr. does not call. If the tumor is not cancerous the probability the Dr. does not call is 1/2. So the probability the Dr. calls is A(0)+ (1- A)(1/2)= 1/2- A/2.
     
  4. Apr 19, 2012 #3
    Re: Probability question: "Ms. Aquina has just had a biopsy ..."

    That's what I got, but a solution manual online got 3/4.
     
  5. Apr 19, 2012 #4
    Re: Probability question: "Ms. Aquina has just had a biopsy ..."

    Chapter 3, Problem 31 from this solution manual http://waxworksmath.com/Authors/N_Z/Ross/AFirstCourseInProb/WriteUp/weatherwax_ross_solutions.pdf [Broken]
     
    Last edited by a moderator: May 5, 2017
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