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AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 8

Lesson 7: The geometric distribution
Math
AP®︎/College Statistics
Random variables and probability distributions
The geometric distribution
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Geometric probability

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Problem

Fatima conducts emissions inspections on cars. She finds that 6% of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.
Find the probability that the first failed inspection occurs on Fatima's 5th inspection.
You may round your answer to the nearest hundredth.
P(C=5)=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
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