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Probability of Randomly Selective Event, Conditional Probability

  1. Jan 27, 2015 #1
    1. The problem statement, all variables and given/known data

    A company has been running a television advertisement for one of its new products. A survey was conducted. Based on its results, it was concluded that an individual buys the product with probability https://utdvpn.utdallas.edu/wwtmp/equations/42/,DanaInfo=.aevnhvE00ljvwm5Ntt.,SSL+b76747aa0afb1816e5979c66ce77851.png [Broken], if he/she saw the advertisement, and buys with probability https://utdvpn.utdallas.edu/wwtmp/equations/1e/,DanaInfo=.aevnhvE00ljvwm5Ntt.,SSL+e895ee9ca85bcbf1e55a96a7573c291.png [Broken], if he/she did not see it. Twenty-five percent of people saw the advertisement.

    a. What is the probability that a randomly selected individual will buy the new product?
    b. What is the probability that at least one of randomly selected five individuals will buy the new product?
    2. Relevant equations
    P(A|B) = P(B|A)P(A)/P(B)

    3. The attempt at a solution
    I already got part A correct.
    The answer is .2
    I am confused on part B probably because of the 1/5 thing. Which equation should I use and where should I start with this one?
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jan 27, 2015 #2
    it didn't post the numbers but the blanks correspond to 56% and 8% respectively
     
  4. Jan 27, 2015 #3

    LCKurtz

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    You have the probability a given person buys is ##.2##. What is the probability they all fail to buy? You could use the binomial distribution but it is easy enough to just calculate.
     
  5. Jan 27, 2015 #4
    Okay so I calculated probability person does not buy as .8 from (1-.56)(.25) + (.92)(.75). But now I am stuck. Where does the five part come in? What should I do next?
     
  6. Jan 27, 2015 #5

    LCKurtz

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    If the probability the first person doesn't buy is ##.8##, and if they are independent, what is the probability the next person doesn't buy? So....
     
  7. Jan 28, 2015 #6

    HallsofIvy

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    If the answer to (a), which you say you got, is p, then the probability that "at least one" will buy is the 1 minus the probability none will buy. The probability that none will buy is (1- p)^5
     
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