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.