SOLUTION: Topic : Discrete Random Variable (Geometric Distribution) In a particular country, 18% of adults wear contact lenses. Adults are randomly selected and interviewed once at a time.

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Question 1203339: Topic : Discrete Random Variable (Geometric Distribution)
In a particular country, 18% of adults wear contact lenses. Adults are randomly selected and interviewed once at a time. Find the probability that the first adult who wears contact lenses is:
(a) One of the first 15 interviewed
(b) Not one of the first nine interviewed
Answer by ikleyn(52776) About Me  (Show Source):
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Topic : Discrete Random Variable (Geometric Distribution)
In a particular country, 18% of adults wear contact lenses.
Adults are randomly selected and interviewed once at a time.
Find the probability that the first adult who wears contact lenses is:
(a) One of the first 15 interviewed
(b) Not one of the first nine interviewed
~~~~~~~~~~~~~~~~~~~ 

(a) It is a typical binomial distribution probability.
    The number of trials is 15; the number of success is 1 (one);
    the probability of success at each individual trial is 0.18.


    You may use a standard probability formula

       P = C%5B15%5D%5E1%2A0.18%2A%281-0.18%29%5E17 = 15%2A0.18%2A0.82%5E17 = 0.0925  (rounded).    ANSWER



(b) The  ANSWER  is P = %281-0.18%29%5E9 = 0.82%5E9 = 0.1676  (rounded).

Solved.