Q366 · Practice questionTechnology-activeComplex familiar4 marks
QUESTION 366 (4 marks)
A component passes a specialised stress test with probability 0.15. Tests of different components are independent. Determine the minimum number of components that must be tested for the probability of at least one pass to be at least 0.90.
For n components, P(at least one pass)=1−0.85n. Require 0.85n≤0.10. Since ln0.85<0, division reverses the inequality: n≥ln0.10/ln0.85=14.16810399…. The minimum integer is 15; n=14 fails.
Exact answers unless rounding is specified; equivalent forms accepted. Retain unrounded intermediate values.
Uses the complementary event.
[1 mark]
Forms the probability inequality.
[1 mark]
Solves with the correct logarithmic inequality direction.
[1 mark]
Rounds up to the minimum integer.
[1 mark]
Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.