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Math Help - Easy probability problem

  1. #1
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    Easy probability problem

    Hey I was working on some HW and couldnt figure something out. The problem is:

    Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.
    (a) Suppose that an operator handles 15 calls. What is the probability that none of the 15 calls result in a reservation? (Give the answer to 3 decimals places.)
    (c) What is the probability that at least one call results in a reservation being made? (Give the answer to 3 decimals places.)

    I cant find the right formula anywhere i know for part a there is a 70% chance each time there will not be a reservation so i tried taking .7^15 but that number is way to small it seems. And i get the same problem on part c. I know the events are independent right?
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  2. #2
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    Quote Originally Posted by ChrisBickle View Post
    Hey I was working on some HW and couldnt figure something out. The problem is:

    Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.
    (a) Suppose that an operator handles 15 calls. What is the probability that none of the 15 calls result in a reservation? (Give the answer to 3 decimals places.)
    (c) What is the probability that at least one call results in a reservation being made? (Give the answer to 3 decimals places.)

    I cant find the right formula anywhere i know for part a there is a 70% chance each time there will not be a reservation so i tried taking .7^15 but that number is way to small it seems. And i get the same problem on part c. I know the events are independent right?
    you're answer should be very small and then very close to 1
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  3. #3
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    Make the probability of booking a reservation X be   Bi(15, 0.3)

    n = 15, p =0.3

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

    For part a) make k = 0 \Rightarrow P(X=0)

    for part c) P(X \geq 1) = P(X=1)+P(X=2)+\dots+P(X=15)

    or 1- P(X=0)
    Last edited by pickslides; October 26th 2009 at 02:09 PM. Reason: Bad Latex
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  4. #4
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    makes sense thank you very much
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