MATH

A local politician claims that 1 in 5 automobile accidents involve a teenage driver. He is advocating increasing the age at which teenagers can drive alone. Over a 2 month period, there are 67 accidents in your city, and only 9 of them involve a teenage driver. If the politician is correct, what is the chance that you would have observed 9 or less accidents involving teenagers?

I have the correct answer, it's 0.0524, but I don't understand how to get this answer. Please help. (I would like to know how to do this by hand and also using a TI-84 calculator)

Thanks in advance.

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  1. Prob(9 or less accidents involving teenagers)
    = P(1 teenager involved) + P(2 teens involved) + ...+ P(9teens involved)
    or
    = 1 - P(no teen involved in 9 accidents)

    Now when you say, "If the politician is correct" I will assume that we should use his/her data, and we would get.
    Prob(teen involved) = .2
    prob(no teen involved) = .8

    P(as stated) = 1 - .8^9 = .86578

    IF we use the actual data
    P(teen involved) = 9/67 = .134328
    P(no teen involved) = 58/67 = .865672 , (note they a add up to 1)

    Prob(as stated) = 1 - (58/67)^9 = .72699

    Somehow I think that I misunderstand the question

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