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Math Help - Geometric Probability Distribution - (Y > 10)

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    Geometric Probability Distribution - (Y > 10)

    Problem:
    An oil prospector drills a succession of holes to find a productive well. The probability he is successful on a given trial is .2. If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

    Here's what I have so far:
    This is a geometric prob. dist. because the sample space contains the countably infinite set of sample points.
    p = 0.2

    P(Y > 10)
    = 1 - [ P(Y = 1), P(Y = 2), ... , P(Y = 10) ]

    I know there is an easier way to do this than adding up the first 10 events, but that's where I'm stuck. I found a similar problem in my textbook where P(Y >= 3), and it had the formula:
    1- p - qp.

    If I do that for this problem: 1 - (0.2) - (0.8)(0.2) = 0.64. I know that value is way too high.
    Does anybody know what I'm doing wrong? Thanks.
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    Re: Geometric Probability Distribution - (Y > 10)

    Quote Originally Posted by crossingdouble View Post
    Problem:
    An oil prospector drills a succession of holes to find a productive well. The probability he is successful on a given trial is .2. If the prospector can afford to drill at most ten wells,

    what is the probability that he will fail to find a productive well?
    (0.8)^{10}
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    Re: Geometric Probability Distribution - (Y > 10)

    Thanks Plato, I got it now.

    I found the correct formula:
    P(Y >= n) = 1 - (1 - ((1 - p)^n))

    For this problem, it simplifies to (0.8)^10.
    And, your approach is actually more simple.
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