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Math Help - Probability question -

  1. #1
    Junior Member
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    Probability question -

    If 85 percent of the autos arriving at the Lincoln Tunnel have either New York or New Jersey license plates, what is the probability that, of the next 20 autos, 2 or fewer (i.e., 0, 1, 2) will bear license plates from states other than New York or New Jersey?

    Here is the answer I came up with...
    0.667

    The answer I came up with is incorrect. I used the 85% divided by 20 then multiplied the answer by 2

    If possible, please help me.

    Thanks,
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  2. #2
    Senior Member Twig's Avatar
    Joined
    Mar 2008
    From
    Gothenburg
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    396
    Hi!

    Let B=\mbox{ "Less than 2/20 cars have different types of plates" }

    What you have is a binomial distribution with success if a car has a different type of plate, and failure if it has a New York och New Jerser plate.

    X=\mbox{ the number of cars with other types of plates }

    With p_{success}=\frac{15}{100} and p_{failure}=\frac{85}{100} , we get

    P(B)=P(X=0)+P(X=1)+P(X=2)=\displaystyle\sum_{k=0}^  {2}\binom{20}{k}\left(\frac{15}{100}\right)^{k}\le  ft(\frac{85}{100}\right)^{20-k} \approx 0.405
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  3. #3
    Junior Member
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    Thank you so much. I understand now the failure vs. success problem. I tried it with another set of numbers and I got the right answer.

    Thank you so much.
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