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Binomial Probabilities

  1. Sep 20, 2013 #1
    1. The problem statement, all variables and given/known data
    You are a real estate salesperson and you currently have 10 listings. Past experience has shown that you will sell approximately 70% of your listings. If sales are independent:

    What is the probability that you make exactly 8 sales?

    2. Relevant equations



    3. The attempt at a solution
    I was wondering why 70% would be used as the the probability for the event of interest... I thought the probability would be the probability of ONE listing that would sell and not 7/10 of your listings. Can someone explain?
     
  2. jcsd
  3. Sep 20, 2013 #2

    Ray Vickson

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    The 70% figure is a long-run average. It really means that the probability of sales is 0.70 per listed property.

    Sometimes problem posers want to sound more conversational and less formal, so instead of saying p = 0.7 per trial they say there is a 70% chance per trial, or sales = 70% of listings; that means 70% on average, not in any individual group of listings.
     
  4. Sep 21, 2013 #3

    haruspex

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    I think there's a little more to it than conversational usage. It is saying that your experience is that you sell 70% of your listings. That's a simple observation. From that you infer that your probability of selling a given listing (in the future) is 0.7. There are certain assumptions in that inference which might not in general be valid.
     
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