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Geometric probability

AP.STATS: UNC‑3 (EU), UNC‑3.E (LO), UNC‑3.E.2 (EK)
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Fatima conducts emissions inspections on cars. She finds that 6, percent 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 5, start superscript, start text, t, h, end text, end superscript inspection.
You may round your answer to the nearest hundredth.
P, left parenthesis, C, equals, 5, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text