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Math Help - Finding probability

  1. #1
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    Finding probability

    If a cell phone company conducted a telemarketing campaign to generate new clients, and the probability of successfully gaining a new customer was 0.08, what are the probabilities that contacting 20 potential customers would result in 0, 1, 2, 3 or 4 new customers?


    I'm not sure how to get started on this question. Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by Marko_02 View Post
    If a cell phone company conducted a telemarketing campaign to generate new clients, and the probability of successfully gaining a new customer was 0.08, what are the probabilities that contacting 20 potential customers would result in 0, 1, 2, 3 or 4 new customers?


    I'm not sure how to get started on this question. Any help would be appreciated.
    Since the events are Bernoulli trials, that would suggest that this follows a binomial probability distribution.

    \displaystyle P(X=k) = \binom{n}{k}P^{k}(1-P)^{n-k}

    For your case n=20,P=0.08

    Can you finish from here?
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    thats very helpful thanks just one thing I don't know if we use different symbols but what does the k represent
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    Quote Originally Posted by Marko_02 View Post
    thats very helpful thanks just one thing I don't know if we use different symbols but what does the k represent
    k is the number of new costumers.

    for example \displaystyle k=0 \implies P(X=0) is the probability that none of the 20 people became new costumers.
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    lets say \displaystyle p=0.08 and \displaystyle n=20

    And \displaystyle P(x=k) = ^nC_k p^k(1-p)^{n-k}

    You need to find

    \displaystyle P(x=0) = ^{20}C_0 0.08^0(1-0.08)^{20-0}=\dots

    \displaystyle P(x=1) = ^{20}C_1 0.08^1(1-0.08)^{20-1}=\dots

    and so on...
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  6. #6
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    Quote Originally Posted by Marko_02 View Post
    If a cell phone company conducted a telemarketing campaign to generate new clients, and the probability of successfully gaining a new customer was 0.08, what are the probabilities that contacting 20 potential customers would result in 0, 1, 2, 3 or 4 new customers?


    I need help getting started on this question. A formula or any help would be appreciated.
    Probability of not gaining a customer=1-0.08=0.92

    Probability that contacting 20 potential customers would result in r new customers is ^{20}C_r(0.08)^r(0.92)^{20-r}.
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  7. #7
    MHF Contributor chisigma's Avatar
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    If we indicate with p the probability of succes in one trial, the probability to have k successes in n trials is...

    \displaystyle P(k,n) = \binom{n}{k} p^{k}\ (1-p)^{n-k} (1)

    In your case is p=.08, n=20 and k=0,1,2,3,4...
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