Page |12 Example: or failure Oil drilling company ventures into various location

Question

Page |12 Example: or failure Oil drilling company ventures into various locations, and their success is independent from one location to another. Suppose the probability o productive well at a 1. Find ny specific location is 0.1. If a driller drills 5 locations, the probability that there will be at least two productive wells. 2. Find the probability that between two and four, inclusive, productive wells will be hit. 3. Compute the 4. The company will stop drilling if they find oil, find the probability hat the probability that only the first two productive wells will be hit. company will find oil in the 7th location

Explanation / Answer

Answer to the question is as follows:

p ( success) = .10

1. P(X>=2) = 1-P(X<2) = 1- (P(X=0) + P(X=1) = 1- ( 5C0*.1^0 *.9^5 + 5C1*.1^1 *.9^4) = 0.91854

2. P(X = 2 to 4) = P(X=2,3,4) = 5C2*.1^2 *.9^3 + 5C3*.1^3 *.9^2+5C4*.1^4 *.9^1 = 0.08145

3. P(first 2 are hit and next 3 aren't) = (.1^2)*(1-.1)^3 = .00729

4. P( at 7th location) = ? = P(fail first 6 times and find in 7th time) = ((1-.1)^6)*(.1)^1 = .05314

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