# Geometric Probability Distribution - (Y > 10)

• Oct 2nd 2012, 02:04 PM
crossingdouble
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.
• Oct 2nd 2012, 02:25 PM
Plato
Re: Geometric Probability Distribution - (Y > 10)
Quote:

Originally Posted by crossingdouble
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?

$(0.8)^{10}$
• Oct 2nd 2012, 06:11 PM
crossingdouble
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.