An oil company conducts a geologival survey that indicates an exploratory oil we

BenoguigoliB

BenoguigoliB

Answered question

2021-09-23

An oil company conducts a geologival survey that indicates an exploratory oil well should have a 23% change of striking oil.
A. What is the probability that the 2nd strike will occur on the 5th attempt?
B. What is the probability that the 7th strike will occur on the 12th attempt?
C. What is the probability that the 11th strike will occur between the 15th and 18th attempt?

Answer & Explanation

hosentak

hosentak

Skilled2021-09-24Added 100 answers

Step 1
Given Information : An oil company conducts a geological survey that indicates an exploratory oil well should have a 23 % chance of striking oil.
Probability of success: p=0.23
Define random variable X denotes number of attempts for striking oil.
Note that X is technically a geometric random variable, since we are only looking for one success.
Since a geometric random variable is just a special case of a negative binomial random variable. Therefore , negative binomial probability formula will be used.
Notation: XNB(p=0.23)
P(X=x)=(beg{array}{c}x1r1end{array})pr(1p)xr
It is the probability of r-th success occurs on x-th trial.
Step 2
(a) Probability that the 2nd strike will occur on the 5th attempt :
Here,
x=5
r=2
Substituting values in the negative binomial probability formula,
P(X=5)=(beg{array}{c}5121end{array})(0.23)2(10.23)52
=0.0966.
(b) Probability that the 7-th strike will occur on the 12-th attempt,
Here,
x=12
r=7
Substituting values in the negative binomial probability formula,
P(X=12)=(beg{array}{c}12171end{array})(0.23)7(10.23)127
=0.004258
(c) Probability that the 11th strike will occur between the 15th and 18th attempt :
Here,
r=11
15X18
Substituting values in the negative binomial probability formula ,
P(15X18)=P(X=15)+P(X=16)+P(X=17)+P(X=18)

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