 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-2/14/a/ii/solution

Passing corresponds to

- π /6 \leq X \leq π /6

in the normalized variable from part (i). Integrating its probability density,

p_{pass} = \frac{1}{2} \int_{- π /6}^{π /6} cos x d x = sin \frac{π}{6} = \frac{1}{2} .

The complementary probability of detecting the fault in one test is also

1/2

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