Simplifying a Probability Question
Date: 08/19/2008 at 08:11:04 From: Aileen Subject: sat A computer software firm maintains a telephone hotline service for its customers. The firm finds that 48% of the calls involve questions about the application of the software, 38% involve issues of incompatibility with hardware and 14% involve the inability to install the software on userís machine. These three categories of problems can be resolved with probabilities 0.90, 0.15, and 0.80 respectively. (1) Find the probability that a call to the hotline involves a problem that cannot be resolved. (2) Suppose that a call to the hotline involves a problem that cannot be resolved. What is the probability that it is an issue of incompatibility with the hardware?
Date: 08/19/2008 at 08:47:37 From: Doctor Ian Subject: Re: sat Hi Aileen, Note that you can eliminate a lot of irrelevant detail by changing the problem to one involving pulling colored and numbered balls from a jar. For example, suppose we have a jar with 1000 balls: 480 are azure (these represent application questions) 380 are crimson (these represent compatibility questions) 140 are indigo (these represent installation questions) Of the 480 azure balls, 90 percent, or 432, are numbered with a 1, representing questions that can be resolved; the the other 48 are numbered with a zero. You can find similar ratios for the other two colors. So now, the question Find the probability that a call to the hotline involves a problem that cannot be resolved. is equivalent to the question What is the probability of pulling out a ball with a zero on it? and the question Suppose that a call to the hotline involves a problem that cannot be resolved. What is the probability that it is an issue of incompatibility with the hardware? is equivalent to the question If I pull out a ball with a zero on it, what is the probability that it is crimson? Can you see why the questions are equivalent? Can you answer them in this form? Try that, and show me the steps you take. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 08/19/2008 at 18:40:11 From: Aileen Subject: Thank you (sat) Thank you a lot you are a great helper. That made the problem a lot easier.
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