Question

1. It is assumed that 25% of the applicants for a certain job Industrial has advanced training in computer programming. Applicants are interviewed, one after another and are selected at random from a large set of aspirants. Determine the probability that:
1) You are the first applicant with advanced training in programming in the fourth interview.
2) The second person with advanced training is the sixth interviewee.
Answer:

2.- A petroleum explorer will drill a series of wells in certain 'area to find a productive well. If The probability of having success in a test is 0.15, determine:
1) The probability that the first productive well will be the fourth hole drilled.
2) The probability that the explorer will not find a productive well if he can only drill at most 6 wells.

**please answer both. THANKS!

Answer 1

Binomial distribution: P(X) = nCx p^x q^n-x​​​​​​​

1. P(an applicant has advanced training in computer programming), p = 0.25

q = 1 - p = 0.75

1) P(first applicant with advanced training in programming in the fourth interview) = P(first 3 applicants do not have training in computer programming) x P(fourth applicant has advanced training in computer programming)

= 0.75³ x 0.25

= 0.1055

2) P(second person with advanced training is the sixth interviewee) = P(exactly one of the first 5 has advanced training in computer programming) x P(sixth applicant has advanced training in computer programming)

= 5C1 x 0.25 x 0.75⁴ x 0.25

= 0.0989

2. P(success), p = 0.15

q = 1 - 0.15 = 0.85

1) P(first productive well will be the fourth hole drilled) = 0.85³ x 0.15

= 0.0921

2) P(the explorer will not find a productive well) = 0.85⁶

= 0.3771